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LIBRARY 

OF  THE 

UNIVERSITY  OF  CALIFORNIA. 

GIFT  -U.VY 

Class 


Gunnery  and  Explosives 

for 

Field  Artillery  Officers 


WASHINGTON 

GOVERNMENT  PRINTING  OFFICE 
1911 


. 

WAR   DEPARTMENT. 
Document  No.  391. 

OFFICE  OF  THE  CHIEF  OF  STAFF. 


WAR  DEPARTMENT, 
OFFICE  OF  THE  CHIEF  OF  STAFF, 

Washington,  May  22,  1911. 

The  following  publication  entitled  "Gunnery  and  Explosives  for 
Field  Artillery  Officers,"  prepared  by  Capt.  William  I.  Westervelt, 
Fifth  Field  Artillery,  under  the  supervision  of  the  Field  Artillery 
Board,  Fort  Riley,  Kans.,  is  herewith  published  for  the  information 
and  guidance  of  the  Field  Artillery  of  the  Regular  Army  and  the 
Organized  Militia  of  the  United  States. 
By  order  of  the  Secretary  of  War: 

LEONARD  WOOD, 
Major  General,  Chief  of  Staff. 


223722 


A  LIST  OF  AUTHORITIES  CONSULTED  IN  THE  PREPARATION  OF  THIS 

VOLUME. 

[Those  of  particular  value  are  marked  with  a  star  (*).- 


IN    ENGLISH. 

Nitro  Explosives.     Sanford. 

*  Essay  on  Shrapnel  Fire  of  Field  Artillery.     Rohne. 
Artillery  Fire.     The  Battery.     Nicholson. 
Manufacture  of  Explosives.     Guttman. 

*  A  Primer  of  Explosives.     Cooper- Key. 

*  Ordnance  and  Gunnery.     Lissak. 

*  Ballistics.     Parts  1,  2,  and  3.     Hamilton. 
The  Modern  High  Explosives.     Eissler. 
Notes  on  Dynamics.     Greenhill. 

*  Modern  Guns  and  Gunnery.     Bethell. 
Field  Artillery  Fire.     White. 

*  Records  of  the  Field  Artillery  Board. 

IN    FRENCH. 

Notes  sur  le  canon  de  75.     Morliere. 

*  Note  sur  le  Tir  Collectif .     French  Ministry  of  War. 
Manuel  de  Tir  de  1'Artillerie  de  Campagne  Allemande.     Jung. 
Tir  Masque.     Touv-enin. 

*  Cours  Elementaire  de  Tir  de  Campagne.     Treguier. 
Pratique  du  Tir  du  Canon  de  75  de  Campagne.     Challeat. 

*  Tir  Masque .     Challeat. 

Le  Tir  de  1'Artillerie  centre  les  Batteries  a  Grands  Boucliers.     Doc- 
quin. 

*  Le  Mecaiiisme  du  Tir  de  1'Artillerie  de  Campagne  a  Tir  Rapide. 

"aillard. 


6  GUNNERY  AND  EXPLOSIVES. 

Emploi  des  Feux  de  1  Artillerie.     Peicin. 

Legons  sur  1' Artillerie.     Alvin. 

*Ballistique  Exterieure  Rationnelle.     Charbonnier. 

*  Lemons  d' Artillerie.     Girardon. 

Revue  d'Artillerie,  vols.  63,  68,  69,  70,  71,  and  73. 

L'Artillerie  de  Campagne  a  Tir  Rapide  et  a  Boucliers.     Campana. 

IN    GERMAN. 

*  Die  Lehre  vom  Schuz  Gewehr  und  Geschutz.    Heydenreich.    Vols. 

1  and  2. 

Die  Explosivstoffe.     Brunswig. 

*Die  Heutige  Feldartillerie  u.  s.  w.     Roskoten.     Vols.  1  and  2. 
Lehrbuch  der  Waffenlehre.     Marschner. 
Artilleristische  Monatshefte,  1907,  pt.  2,  and  1908,  pt.  2. 

*  Zielerkundung  der  Artillerie.     Seeger. 

*  Die   Richt-    und    Schiess-    Ausbildung  der    Feldartillerie    unter 

Berucksichtung  des  Feldartillerie-Gerats.     Landau-er. 

*  Die  Feuertatigkeit  der  8  cm.  Feld  Kannonen  Batterien.     Eisner. 


TABLE  Or  CONTENTS. 


PART  I. 

GTJNNERY. 

Par. 

CHAPTER  I. — The  three-inch  field  artillery  materiel 1-8 

II. — The  trajectory  in  vacuo 9-12 

III.— The  range  table 13-26 

IV. — Ammunition  for  the  light  field  gun 27-30 

.  V. — Calculation  of  the  elements  of  fire 31-38 

VI. — Rapid  calculation  of  the  elements  of  the  tra- 
jectory   39-47 

VII. — Accuracy  of  fire  and  causes  affecting  it 48-57 

VIII.— The  single  shrapnel 58-64 

IX. — The  effect  of  a  group  of  shrapnel 65-70 

X.— Ranging 71-75 

XI. — Preparation  and  conduct  of  fire 76-78 

PART  II. 

EXPLOSIVES. 

CHAPTER  I. — Explosives 1-12 

II. — High  explosives 13-19 


APPENDIX  A. — The  Greek  alphabet. 

B. — Range  table  for  3-inch  field  gun. 

C. — Examination  questions. 

D. — Geometrical  illustration  of  parallax  method. 


GUNNERY  AND  EXPLOSIVES  FOR  FIELD  ARTILLERY 
OFFICERS. 


Part  I.— GUNNERY. 


CHAPTER  I. 

THE   THREE-INCH   FIELD   ARTILLERY   MATERIEL. 

1.  The  gun. — The  gun  with  which  this  text  is  primarily  con- 
cerned is   the  3-inch  field  gun.     A   thorough  knowledge  of  this 
weapon  is  of  prime  importance  to  the  field  artilleryman  and  is  to  be 
gained  by  a  study  of  the  Handbook  of  the  3-inch  Field  Artillery 
Materiel.     In  this  study  it  is  essential  that  reference  be  made  to  the 
gun  itself  or  to  other  parts  of  the  materiel,  for  in  this  way  only  is  it 
possible  to  verify  concretely  the  facts  set  forth  in  the  handbook. 
It  should  be  borne  in  mind  that,  without  the  gun  itself,  field  artillery 
has  no  part  to  play;  for  this  reason  the  gun  is  the  initial  field  artillery 
conception,  to  be  followed  in  order  by  a  knowledge  of  its  ammuni- 
tion, its  equipment,  and  its  mobility.     A  knowledge  of  the  materiel, 
a  proper  understanding  of  its  limitations  and  a  keen  desire  to  learn 
its  proper  use,  are  the  fundamentals  upon  which  subsequent  expe- 
rience builds  the  accomplished  field  artilleryman. 

2.  General  remarks  concerning  the  materiel. — The  introduc- 
tion of  smokeless  powder  and  of  accurate   long  range  small   arms 
made  obsolete  the  old  idea  of  battle  fields.     Concealed  positions 
became  the  rule  rather  than  the  exception;  changes  of  position 
involved  speed  arid  a  minimum  of  exposure.     The  old  type  of 
weapon  was  useless  under  the  new  conditions  and  it  was  mechan- 
ically incapable  of  taking  advantage  of  the  fleeting  moments  during 
which  an  enemy  was  exposed.     The  problem  of  bringing  the  field 
artillery  weapon  up  to  date  was  solved  when  the  long-recoil  carriage 
was  perfected.     On  this  carriage  the  gun  recoils  without  objection- 
able derangement  of  its  laying,  returning  after  firing  to  a  position 
so  near  its  former  one  that  it  may  be  layed  accurately  without  loss 
of  time. 


10  GUNNERY  AND  EXPLOSIVES. 

3.  Considerations  affecting  the  design. — Without  introducing 
the  idea  of  mobility,  gun  power  would  be  the  ruling  factor  in  the 
design  of  a  light-artillery  weapon,  hence    the  ordnance  engineer 
would  need  little  more  than  a  reference  to  his  designs  of  weapons 
intended   for  coast  defense.     Mobility,   however,   is  a  factor — an 
essential  one — and  for  this  reason  the  field-artillery  service  finds  itself 
restricted  to  that  gun  power  which  may  be  pulled  from  place  to  place 
by  horses.     That  the  power  of  the  horse  thoroughly  dominates  the 
situation  may  be  discerned  in  an  analysis  of  the  light  field  artillery 
of  all  nations — the  materiel  is  practically  standardized.     Although 
it  is  a  fact  that  the  field  artillery  weapon  is  limited  by  questions 
of  mobility,  it  will  be  shown  that,  notwithstanding  its  necessarily 
curtailed  power,  it  is  rarely  if  ever  used  to  the  full  theoretical  limit. 
The  questions  of  ammunition  supply,  observation  of  fire,  loss  of  time 
not  attributable  to  the  materiel,  etc.,  enter  largely  into  its  practical 
employment. 

4.  Power  of  the  weapon. — Shrapnel  is  the  principal  ammunition 
used  by  the  field  artillery,  and  with  the  adoption  of  the  high  explo- 
sive shrapnel,  or  unit  projectile,  will  be  the  only  projectile  for  the 
light  field  weapon.     As  the  particular  function  of  the  shrapnel  is 
to  carry  a  number  of  bullets  to  a  distance  from  the  gun,  there  to  dis- 
charge them  with  killing  energy,  the  gun  should  be  designed  with 
a  view  to  permitting  the  highest  attainable  shrapnel  efficiency. 
The  3-inch  field  gun  is  admirably  suited  to  the  above  condition. 

The  maximum  range  of  a  service  shrapnel  is  well  in  excess  of  6,000 
yards,  up  to  which  point  its  remaining  velocity,  when  augmented 
by  that  due  to  the  shrapnel  bursting  charge,  is  sufficient  to  produce 
killing  effect  upon  horses  and  men.  The  initial  velocity  of  the  gun 
under  consideration  is  1,700  feet  per  second.  Such  velocity  is 
small  when  compared  with  that  of  high-power  coast-defense  guns, 
but  it  is  ample  for  the  purpose.  Little  or  no  advantage  would  accrue 
from  higher  velocities  as  the  projectile  is  deficient  in  power  of  pene- 
tration and  too  small  for  serious  percussive  effect  against  even  tem- 
porary entrenchments.  The  limit  of  the  necessary  power  of  light 
field  artillery  has  been  reached  when  opposing  personnel  is  being 
annihilated,  when  opposing  materiel  of  like  power  is  being  de- 
stroyed, or  when  the  fire  from  moderately  entrenched  positions  is 
being  neutralized. 

5.  Rapidity  of  fire. — The  questions  of  mobility  and  power  having 
been  treated,  some  consideration  of  the  speed  and  facility  with 
which  the  service  weapon  performs  its  function  should  follow.     As 


GUNNERY  AND  EXPLOSIVES.  11 

previously  stated,  the  important  feature  making  for  rapidity  of  fire 
is  the  return  of  the  gun  after  firing  to  its  former  position.  Any 
small  derangement  may  be  corrected  by  small  and  quick  changes 
in  the  traversing  and  elevating  mechanisms.  By  an  examination 
of  the  breech  mechanism,  fuse  setter,  and  readily  adjusted  devices 
for  laying,  it  will  be  seen  that  the  idea  of  a  rapid-fire  machine  has 
been  mechanically  expressed  in  the  service  3-inch  field  artillery 
materiel.  Fixed  ammunition  and  easily  set  fuses  also  contribute 
to  rapid  fire. 

6.  Pointing  the  gun. — A  gun  must  be  pointed  in  such  direction 
and  elevated  to  such  degree  that  a  projectile  fired  from  it  will  hit 
the  target.  In  order  to  regulate  the  direction,  a  fixed  line  is  estab- 
lished, and  the  axis  of  the  gun  is  given  such  direction  in  relation  to 
this  fixed  line  as  will  result  in  hits  on  the  target  when  the  gun  is 
properly  elevated.  The  fixed  line  becomes  the  line  from  gun  to 
target  in  direct  laying  and  from  gun  to  aiming  point  in  indirect 
laying.  The  appliances  provided  for  pointing  and  laying  the  3-inch 
fieldpiece  include  line  sights,  the  adjustable  or  tangent  sight,  the 
panoramic  sight,  and  the  range  quadrant,  all  of  which  are  fully 
described  in  the  handbook.  The  sighting  apparatus,  except  in  case 
of  the  line  sights,  is  attached  to  nonrecoiling  parts  of  the  gun  car- 
riage and  remains  in  place  during  firing.  As  the  carriage  does  not 
move,  the  gunner,  with  elevating  and  traversing  hand  wheels  con- 
veniently at  hand,  finds  the  operation  of  sighting  a  continuous  one. 

The  elevation  and  direction  are  given  by  moving  the  cradle  to 
which  the  sight  and  quadrant  are  attached. 

This  system  does  not  have  the  independent  line  of  sight  used  by 
the  French.  In  that  system  the  elevation  of  the  gun  for  range  is 
made  above  the  rocker  or  top  carriage,  while  the  angle  of  site  is  set  off 
by  moving  the  top  carriage.  This  method  necessitates  the  setting  of 
an  angle  of  site  device  for  all  direct  as  well  as  for  indirect  laying. 

Some  form  of  telescopic  sight  is  necessary,  in  view  of  the  great 
range  of  the  field  gun  and  for  the  reason  that  indirect  laying  re- 
quires a  sight  permitting  rapid  laying  of  the  gun  when  the  target  is 
hidden.  These  two  requisites  are  combined  in  the  panoramic  sight, 
which  is  a  telescopic  sight  so  fitted  with  reflectors  and  prisms  that 
the  observer,  with  his  eye  at  an  eyepiece  fixed  in  position,  may 
bring  into  the  field  of  view  any  object  upon  the  horizon,  the  image 
appearing  magnified,  but  otherwise  as  if  viewed  directly  by  the 
unaided  eye.  Due  to  the  fact  that  with  the  telescopic  sight  the 
image  of  the  target  or  aiming  point  is  in  the  same  plane  as  the  cross 


12  GUNNERY  AND  EXPLOSIVES. 

wires,  this  sight  is  more  accurate  than  the  tangent  sight  and  requires 
less  experience  to  use. 

The  range  quadrant  is  for  the  purpose  of  setting  off  the  proper 
range  during  indirect  laying.  For  direct  laying  the  sights  are  gen- 
erally used,  but  for  indirect  laying  the  range  quadrant  must  be  used, 
since  the  angle  of  site  of  an  aiming  point  bears  no  fixed  relation  to 
that  of  the  target. 

In  order  to  take  full  advantage  of  the  great  range  and  accuracy  of 
the  service  materiel  and  of  the  refinements  of  the  sighting  arrange- 
ments, a  battery  commander's  telescope  has  been  provided.  This 
telescope  is  of  the  general  form  of  the  panoramic  sight,  but  more 
powerful,  and,  with  its  all-around  motion  in  azimuth  and  limited 
motion  in  elevation,  becomes  a  satisfactory  angle-measuring  instru- 
ment. The  scales  of  the  telescope,  sights,  and  range  quadrant  are 
so  graduated  that  a  reading  may  be  transferred  from  one  instrument 
to  another  without  computation  or  reference  tables. 

The  officer  conducting  the  fire  is  furnished  with  appropriate 
observing  glasses  and  with  proper  equipment  for  the  transmission  of 
his  commands. 

7.  Gunnery  as  applied  to  field  artillery. — The  field  artillery- 
man, in  the  practice  of  his  profession,  does  not  require  a  great  knowl- 
edge of  the  mathematics  of  gunnery.     As  a  matter  of  culture  such 
knowledge  is  desirable,  but  it  should  not  be  sought  at  the  expense 
of  more  practical  knowledge.     The  materiel  issued  for  use  in  the 
field  artillery  is  the  result  of  thoughtful  design  and  thorough  test 
and  may  be  taken  as  representative,  at  least,  of  the  best  modern 
conception  of  such  materiel.     A  battery  of  3-inch  field  guns  is  a 
plant  of  •  no  small  importance,   the  proper  management  of  which 
requires  intelligence  and  unflagging  zeal.     Conditions  are  such  that 
no  absolute  criterion  of  excellence  may  be  established  in  the  case  of 
field  batteries.     But  that  battery  which  has  been  perfected  in  fire 
discipline  and  whose  commanding  officer  comprehends  minutely  the 
purpose  of  each  mechanism  of  fire  and  is  an  adept  in  applying  his 
knowledge  may  be  said  to  represent  the  aim  of  practical  gunnery. 
Before  such  an  organization  can  be  evolved  the  materiel  itself  must 
be  thoroughly  understood. 

8.  Methods  of  instruction. — The  purpose  of  this  text  is  to 
suggest  such  topics  as  are  important  to  an  officer  of  field  artillery. 
The  information  contained  herein  should  be  augmented  by  lectures 
from  capable  and  well-informed  instructors  and  by  consulting  the 
authoritative  works  to  which  reference  has  already  been  made. 


CHAPTER  II. 

THE    TRAJECTORY   IN   VACUO. 

9.  Trajectory. — As  ordinarily  understood  by  practical  artillery- 
men, the  path  followed  by  a  projectile  during  its  exterior  flight  from 
gun  to  target  is  known  as  its  trajectory.  Such  conception  is  quite 
complete  in  so  far  as  the  field  artilleryman  is  concerned,  as  he  has 
no  control  over  that  portion  of  the  projectile's  motion  termed  its 
interior  flight.  It  will  be  assumed,  therefore,  that  ammunition  issued 
for  use  in  the  field  artillery  is  of  such  nature  that  successive  pro- 
jectiles of  the  same  type,  fired  under  the  same  conditions,  will  have 


the  same  trajectory.  While  the  assumption  is  not  strictly  correct, 
as  will  be  shown  in  a  succeeding  chapter,  yet  it  is  sufficiently  true 
for  purposes  of  discussion  and,  in  the  preliminary  understanding  of 
firing  terms,  should  be  adhered  to  rigidly. 

10.  Definitions. — The  trajectory,  bdf,  figure  1,  is  the  path  of 
the  projectile  from  gun  to  target. 

The  range,  &/,  is  the  distance  from  the  muzzle  of  the  gun  to  the 
target. 

13 


14  GUNNERY  AND   EXPLOSIVES. 

The  line  of  sight,  abf,  is  the  right  line  passing  through  the  sights 
and  target  or  aiming  point. 

The  line  of  departure,  fee,  is  the  prolongation  of  the  axis  of  the  bore 
at  the  instant  the  projectile  leaves  the  gun. 

The  plane  of  fire,  or  plane  of  departure,  is  the  vertical  plane 
through  the  line  of  departure. 

The  angle  of  site,  or  angle  of  position,  e,  is  the  angle  made  by  the 
line  joining  gun  and  target  with  the  horizontal. 

The  angle  of  departure,  <£,  is  the  angle  made  by  the  line  of  depar- 
ture with  the  line  joining  gun  and  target. 

The  quadrant  angle  of  departure,  0-f-e,  is  the  angle  made  by  the 
line  of  departure  with  the  horizontal.  This  is  greater  than  the  angle 
of  departure  when  the  target  is  above  the  horizontal  and  smaller 
when  the  target  is  below  the  horizontal. 

The  angle  of  elevation,  fy ',  is  the  angle  between  the  line  joining 
gun  and  target  and  the  axis  of  the  piece  when  the  gun  is  laid. 

The  jump,  j,  is  the  angle  between  the  line  of  departure  and  the 
axis  of  the  gun  before  firing.  The  gun  and  its  carriage  are^made  up 
of  elastic  parts  which  yield  to  a  slight  extent  under  the  action  of  the 
firing  stresses,  the  resulting  effect  being  a  small  displacement  of  the 
axis  of  the  piece  after  firing.  The  angle  of  departure  is  usually  greater 
than  the  angle  of  elevation. 

The  point  of  fall,  or  point  of  impact,/,  is  the  point  at  which  the  pro- 
jectile strikes. 

The  angle  of  fall,  o>,  is  the  angle  made  by  the  tangent  to  the  trajec- 
tory with  the  line  joining  gun  and  target  at  the  point  of  fall. 

Initial  velocity  is  the  velocity  of  the  projectile  at  the  muzzle. 

Remaining  velocity  is  the  velocity  of  the  projectile  at  any  point  of 
the  trajectory. 

The  drift,  kf,  is  the  departure  of  the  projectile  from  the  plane  of 
fire,  due  principally  to  the  resistance  of  the  air  and  to  the  projectile's 
rotation. 

11.  The  trajectory  in  racuo. — In  order  to  understand  the 
trajectory  in  air  the  motion  of  a  projectile  in  vacuo  will  first  be  con- 
sidered. Under  this  assumption  all  the  variable  incidents  of  service 
firing  are  avoided  and  the  mind  is  left  at  liberty  to  form  a  conception 
of  the  path  followed  by  a  mass  projected  into  space  and  acted  upon 
by  the  earth's  attract' on  solely.  The  projection  into  space  is  accom- 
plished through  the  action  of  the  expanding  gases  of  the  propelling 
charge,  which  action  imparts  velocity  to  the  projectile .  This  velocity 


GUNNERY  AND  EXPLOSIVES. 


15 


is  known  as  the  initial 
or  muzzle  velocity  and 
is  measured  in  feet  per 
second.  By  assigning 
a  definite  value  to  the 
initial  velocity  and 
knowing  the  direction 
of  motion  at  its  origin, 
the  trajectory  in  yacuo 
becomes  determinate 
and  can  be  easily 
plotted.  At  this  period 
of  the  discussion  it 
should  be  noted  that 
until  the  direction  of 
motion  is  assumed  the 
problem  remains  inde- 
terminate. This  direc- 
tion of  motion  is  re- 
ferred to  a  right  line 
joining  both  ends  of  the ' 
trajectory,  and  makes 
with  it  an  angle  known 
as  the  angle  of  depar- 
ture. 

THE  TRAJECTORY  IN 
VACUO,  ILLUSTRATED 
GRAPHICALLY. 

At  the  origin  of  the 
motion  about  to  be 
considered,  let  it  be 
assumed  that  the  pro- 
jectile has  a  velocity 
of  824.6  feet  per  second 
along  the  line  OB  (fig. 
2),  making  an  angle  of 
14°  2X  10/x.l  with  the 
horizontal  OX,  This 
would  be  800  feet  per 


T 


1 


•I* 


16  GUNNERY  AND  EXPLOSIVES. 

.  second  in  a  horizontal  direction  and  200  feet  per  second  in  a 
vertical  direction.  OZ  is  normal  to  OX  and  the  trajectory  OabcdX 
lies  in  the  vertical  plane  XZ.  The  discussion  of  the  trajectory  in 
vacuo  presupposes  that  the  only  forces  acting  is  that  of  gravity— 
hence  the  laws  of  gravity -apply. 

It  is  known  that  a  body  falling  freely  drops  a  distance  of  approxi- 
mately 16  feet  in  the  first  second  after  gravity  begins  to  act.  There- 
after the  distance  increases  according  to  the  following  formula: 

S  (distance  dropped )=16£2 

in  which  t  stands  for  the  number  of  seconds  during  which  the  body 
has  been  falling  under  the  action  of  gravity. 

Referring  to  figure  2,  it  will  be  seen  that  except  for  the  action 
of  gravity  the  projectile  would  have  proceeded  along  its  original 
right  line  of  departure,  OB.  According  to  the  law,  however,  its 
position  at  the  end  of  any  assumed  second  will  be  I6t2  feet  below 
the  line  of  departure.  The  problem  is  solved  graphically  in  figure  2. 

It  is  generally  known  that  a  mass  falling  from  rest  under  the  action 
of  gravity  will  cover  a  space  of  16  feet  in  the  first  second.  This 
can  be  demonstrated  practically  by  dropping  a  stone  and  timing 
its  fall.  It  will  be  found  that  the  stone  will  drop  64  feet  in  2  sec- 
onds and  144  feet  in  3  seconds. 

From  these  facts  we  may  proceed  to  the  analysis  of  the  relations 
existing  between  falling  bodies  and  the  earth.  Under  what  con- 
ceivable law  will  a  mass  fall  16  feet  in  1  second,  64  feet  in  2  seconds, 
and  144  feet  in  3  seconds?  Certainly  its  velocity  or  speed  can 
not  be  uniform,  for  during  the  second  second  it  falls  48  feet  and 
during  the  third  second  it  falls  80  feet.  We  therefore  reach  the 
conclusion  that  a  falling  body  gains  speed  as  it  falls.  We  know 
that  the  body  which  starts  from  rest  or  zero  velocity  falls  16  feet 
in  the  first  second,  hence  during  this  second  it  must  have  averaged 
a  velocity  of  16  feet  per  second,  or  must  have  acquired  at  the  end 
of  this  second  a  velocity  of  32  feet  per  second.  In  the  second  sec- 
ond, since  a  force  has  the  same  effect  on  a  body  at  rest  or  in  motion, 
it  again  drops  16  feet  due  to  gravity;  but  it  also  drops  32  feet  due 
to  the  velocity  it  had  at  the  end  of  the  first  second,  or  48  feet.  The 
body  falls  three  times  as  far  in  the  second  second  as  it  does  in  the 
first  second,  hence  its  average  speed  during  this  second  is  48  feet 


GUNNERY  AND  EXPLOSIVES.  17 

per  second;  since  it  started  with  a  velocity  of  32  feet  per  second 
at  the  beginning  of  the  second  second,  it  must  have  acquired  a 
speed  of  64  feet  per  second  at  the  end  of  the  second  second  in  order 
to  have  averaged  48  feet  per  second  during  that  second.  It  will 
be  seen,  therefore,  that  a  falling  body  has  a  variable  speed  which 
increases  at  the  rate  of  32  feet  per  second  and  that  the  velocity  at 
any  time  may  be  found  from  the  following  formula: 

V  (velocity  at  any  time)  =  32  t 

in  which  t  stands  for  the  number  of  seconds  during  which  the  body 
has  been  falling  under  the  action  of  gravity.  If  the  body  had 
velocity  before  gravity  commenced  to  act  it  must  be  considered  also. 
For  instance,  if  a  body  is  thrown  vertically  downward  at  a  speed  of 
500  feet  per  second,  at  the  end  of  the  first  second  its  speed  will  be  532 
feet  per  second .  Conversely,  if  a  body  is  projected  vertically  upward 
at  a  speed  of  500  feet  per  second,  at  the  end  of  the  first  second  its 
speed  will  be  468  feet  per  second ;  in  other  words,  gravity  adds  to  or 
subtracts  from  already  existing  vertical  velocity  at  the  rate  of  32 
feet  per  second. 

A  study  of  figure  2,  in  connection  with  the  above  remarks  will 
reveal  the  simplicity  of  the  application  of  the  law  of  gravity.  For 
instance,  the  particular  projectile  considered  has  an  initial  velocity 
of  200  feet  per  second  in  the  upward  vertical  direction ;  gravity  takes 
away  from  this  velocity  32  feet  per  second,  hence,  in  two  hundred 
divided  by  32,  or  6|  seconds,  the  projectile  will  have  no  upward 
velocity  and  will  be  found  at  the  summit  or  topmost  point  of  its 
trajectory. 

In  a  similar  way  it  may  be  shown  that  the  total  time  of  flight  is 
12J  seconds,  and  that  the  range  is  10,000  feet. 

12.  Rigidity  of  the  trajectory. — According  to  the  principle  of 
the  rigidity  of  the  trajectory,  which  can  be  demonstrated  mathe- 
matically, the  relations  existing  between  the  trajectory  and  the  line 
representing  the  range,  are  sensibly  the  same  whether  the  range  be 
horizontal  or  inclined  to  the  horizon,  provided  that  the  quadrant 
angle  of  departure  is  small.  That  is  to  say  that,  considering  </>-{-£,  as 
small,  in  figure  1,  if  the  trajectory  6c//and  the  range  6/were  revolved 
about  the  point  b  until  bf  were  horizontal,  the  relation  of  the  tra- 
jectory to  bf  would  not  change.  A  trajectory  calculated  for  a  hori- 

96609°— 11 2 


18  GUNNERY  AND  EXPLOSIVES. 

zontal  range  equal  to  bf  would  then  answer  as  the  trajectory  for  the 
actual  inclined  range  bf.  In  other  words,  if  the  angle  of  departure 
necessary  to  reach  a  certain  point  at  a  horizontal  range,  x,  from  the 
gun  and  on  the  same  level,  is  known,  it  will  only  be  necessary  in 
order  to  reach  another  point  h  feet  below  the  former  and  at  the  same 
horizontal  range,  x,  to  subtract  from  the  first  angle  of  departure  the 
angle  of  site. 

It  follows  from  this  principle  that,  within  reasonable  limits,  the 
trajectory  is  subservient  to  the  will  of  the  officer  conducting  the  fire. 
The  action  of  a  fire  hose  throwing  a  stream  of  water  under  constant 
pressure  is  a  homely  but  useful  conception  of  what  may  be  done 
with  the  trajectory  of  guns  firing  at  comparatively  small  quadrant 
angles  of  departure. 


CHAPTER  III. 


THE    RANGE    TABLE. 

13.  The  trajectory  in  air. — Due  to  atmospheric  resistance  to 
the  projectile's  motion,  the  trajectory  in  air  differs  from  the  hypo- 
thetical trajectory  in  vacuo.  A  proper  conception  of  the  latter 
assists  in  understanding  the  former.  Motion  in  a  resisting  medium 
is  merely  a  modified  form  of  unresisted  motion  and,  though  its  laws 
may  be  somewhat  complex,  yet,  for  any  set  of  conditions  to  bcJ  met 
with  in  practice,  they  are  readily  deduced.  Fired  with  the  same 
angle  of  departure,  a  projectile  resisted  by  the  air  will  have  a  shorter 
range  than  the  projectile  in  vacuo;  the  latter  has  no  force  acting 
upon  it  except  that  vertically  downward  and  due  to  grarity,  whereas 
the  former  is  continuously  retarded  by  the  pressure  of  the  air  in  front 
of  it  and  the  friction  of  air  on  its  sides.  In  the  table  below  will  be 
found  a  comparison  of  certain  elements  of  the  trajectory  in  air  with 
the  trajectory  in  vacuo.  The  information  concerning  the  trajectory 
in  air  is  taken  from  the  range  table  (Appendix  B).  The  trajectories 
in  vacuo  have  been  computed  for  the  five  angles  of  departure  corre- 
sponding to  ranges  in  air  of  1,000,  2,000,  3,000,  4,000,  and  5,000 
yards. 


Angle  of  " 
departure. 

Muzzle 
velocity. 

Range. 

Maxi- 
mum or- 
dinate. 

Time  of 
flight. 

Air 

1    11  2 

Ft.  sec. 
1  700 

Yards. 
1  000 

Feet. 
17.3 

Sees. 
2.07 

Vacuo  

1    11.2 

1,700 

1,245 

19.4 

2.20 

Air 

2    56  7 

1  700 

2  000 

93  1 

4.46 

Vacuo. 

2    56.7 

1,700 

3,089 

119.2 

4.75 

Air  

5    12 

1,700 

3,000 

257.0 

7.83 

Vacuo 

5    12 

1,700 

5,434 

370.9 

9.63 

Air  

7    54.  2 

1,700 

4,000 

536.0 

11.25 

Vacuo 

7    54  2 

1  700 

8  200 

853  8 

14.61 

Air... 

11    10.1 

1,700 

5,000 

975.0 

15.12 

Vacuo 

11     10  1 

1  700 

11  440 

1,694.0 

20.58 

19 


20  GUNNERY  AND  EXPLOSIVES. 

Some  idea  may  be  formed  of  the  resistance  of  the  air,  when  it  is 
seen  that  a  range  of  8,200  yards  in  vacuo  corresponds  to  4,000  yards 
in  air. 

14.  Range  tables. — Range  tables  set  forth  in  a  convenient  form 
certain  facts  pertaining  to  the  trajectory  of  a  projectile  in  air.     Such 
tables  are  usually  based  upon  actual  firing  at  the  proving  grounds. 
For  instance,  the  shrapnel  range  table  (Appendix  B)  was  prepared 
approximately  as  follows:  A  sufficient  number  of   shrapnel  fused 
with  the  service  fuses  of  the  same  lot  were  secured  for  the  test.      Ten 
rounds  each  were  fired  to  burst  on  impact  at  ranges  of  approximately 
1,500,  2,500,  3,500,  4,500,  and  5,500  yards  and  all  the  incidents  of 
firing  were  carefully  observed.     The  angles  of  departure  and  the 
muzzle  velocities  of  the  rounds  in  each  group  were  as  nearly  as 
possible  the  same.     The  ranges  were  accurately  measured  and  at  the 
close  of  the  firing  it  became  known  that  certain  angles  of  departure 
would  assure  certain  horizontal  ranges.     Having  five  ranges  accu- 
rately determined   by  firing,  the  range  table  was  completed   by 
interpolation   according   to    known    mathematical   methods.     The 
range  table  is  the  basis  for  graduation  of  the  rear  sight  and  the  range 
quadrant.     The  probable  behavior  of  fuses,  which  ordinarily  are 
supposed  to  be  adjusted  so  as  to  burst  in  air,  is  likewise  determined 
by  experiment,  as  the  graduations  on  the  fuse  and  on  the  fuse  setter 
depend  upon  the  range  of  a  shrapnel  to  its  bursting  point. 

15.  Range  table  for  3 -inch  field  gun. — An  examination  of  the 
range  table  for  the  3-iiich  field  gun  will  show  the  plan  of  its  con- 
struction.    The  ranges  are  tabulated  for  every  100  yards  up  to  and 
including  6,500  yards,  and  are  the  horizontal  ranges  corresponding 
to  the  proper  angles  of  departure,  conditions  being  normal.     By 
"normal  conditions"  is  meant: 

That  the  gun  is  on  the  same  level  as  the  target. 

That  the  muzzle  velocity  is  1,700  feet  per  second. 

That  each  projectile  is  an  exact  duplicate  of  all  others. 

That  there  is  no  wind. 

That  a  standard  barometric  condition  prevails  during  the  firing 
for  range  data. 

There  will  be  departures  from  the  ideal  conditions.  Theoretically, 
such  departures  should  be  considered  during  firing,  but  practically 
the  necessary  corrections  are  applied  boldly  at  first,  and  then  more 
carefully  until  the  final  laying  of  the  piece  and  the  setting  of  the  fuze 
give  the  results  desired.  For  instance,  on  a  windy  day  when  the 


GUNNERY  AND  EXPLOSIVES.  21 

barometer  reading  is  high  and  the  thermometer  low,  the  officer  con- 
ducting the  fire  would  avoid  the  consideration  of  each  individual 
departure  from  normal  conditions,  by  changing  the  angle  of  departure, 
the  deflection  of  his  piece  and  the  setting  of  his  fuses,  until  his  obser- 
vation indicated  satisfactory  range,  direction,  and  height  of  burst. 

In  the  field  reference  to  a  table  will  be  rare,  as  the  instruments 
used  in  laying  the  gun  for  elevation  and  direction  and  for  fuse 
setting  have  been  designed  to  express  mechanically  the  facts  given  in 
the  range  table. 

16.  Angle  of  departure. — The  second  and  third  columns  in  the 
range  table  set  forth  the  angle  of  departure  corresponding  to  each 
tabulated  value  of  the  range.     This  angle  is  made  up  of  the  proper 
elevation  for  the  horizontal  range  considered  plus  the  angle  of  jump, 
which  latter  angle  increases  as  the  angle  of  elevation  of  the  piece  is 
increased .     In  measuring  the  angle  of  jump  the  gun  carriage  is  placed 
upon  a  platform,  the  quadrant  angle  of  elevation  carefully  applied 
to  the  piece,  which  is  then  fired.  A  screen  of  paper  placed  at  a  known 
distance  in  front  of  the  gun  and  away  from  the  effect  of  the  blast 
will  show  the  hole  made  by  the  projectile.     It  will  be  found  that  the 
center  of  the  hole  is  above  the  line  passing  through  the  axis  of  the 
piece  before  firing.     Knowing  the  proper  distance  from  gun  to  screen, 
the  jump  may  be  computed. 

17.  One  minute,  in  yards  of  range. — The  fifth  column  of  the 
range  table  is  of  interest  as  indicating  the  error  in  range  which  may 
be  expected  from  an  incorrect  laying  for  elevation.     The  value  in 
range  of  one  minute  in  the  angle  of  departure  decreases  with  the 
range.     The  sixth  column  gives  similar  information  in   terms  of 
mils. 

18.  A  X  for  ±10  f.  s.  M.  V.— As  stated  before,  the  range  table 
is  based  upon  a  muzzle  velocity  of  1,700  feet  per  second.     Any 
variation  in  this  velocity  causes  a  corresponding  increase  or  decrease 
in  the  range.     As  ammunition  is  issued  to  the  field  artillery  in  rounds 
already  made  up  ready  for  firing,  variations  in  muzzle  velocity  can 
not  ordinarily  be  attributed  to  improper  handling  by  troops.     How- 
ever, care  must  be  taken  not  to  allow  a  round  of  ammunition  to  remain 
in  the  bore  of  a  gun  which  has  been  heated  by  firing,  as  an  increase 
in  temperature  of  the  powder  before  firing  will  raise  the  muzzle  veloc- 
ity.    The  round  of  ammunition  should  be  handled  with  reasonable 
care  to  avoid  rupturing  the  igniting  charge  of  black  powder.     The 
rotating  band  should  be  protected  from  mutilation  and  the  bore  of 


22  GUNNERY  AND  EXPLOSIVES. 

the  gun  should  be  kept  reasonably  clean.  Further  than  these 
precautions,  it  is  not  practicable  in  the  field  to  take  account  of 
variations  in  muzzle  velocity.  The  effect  of  such  variations  are 
corrected  by  the  bracketing  system. 

19.  AX  for  AC=±1/10.— C  is  the  ballistic  coefficient  of  the 
projectile  under  the  assumed  conditions  of  firing.     A  variation  in 
these  conditions  produces  a  corresponding  variation  in  C.     It  must 
be  understood  that  firing  is  rarely  conducted  under  the  conditions 
upon  which  the  range  table  is  based.     The  range  table  standard 
barometric  height,  thermometer  reading,  etc.,  do  not  exist  in  actual 
practice  except  as  a  matter  of  chance.     An  examination  of  this  im- 
portant factor  in  the  formula  for  the  range  should  be  interesting. 

di 

~3' 
in  which, 

d1  is  the  standard  or  range  table  density  of  the  air. 

d  the  density  for  the  time  considered. 

PC  the  coefficient  of  reduction. 

d  the  diameter  of  the  projectile  in  inches. 

w  the  weight  of  the  projectile  in  pounds. 

It  will  be  seen,  therefore,  that  C  will  change  whenever  d,  /?c,  d, 
and  w  change;  d  and  w  are  the  diameter  and  weight,  respectively, 
of  the  service  3-inch  projectile,  and  may  be  assumed  not  to  vary; 
PC  is  a  coefficient  determined  by  experiment  with  the  particular 
kind  of  projectile,  and  may  be  assumed  to  remain  constant.  The 
principal  variation  in  C  is  therefore  due  to  d  or  changes  in  atmos- 
pheric conditions.  Tables  have  been  prepared  from  which,  know- 
ing the  height  of  the  barometer  and  the  temperature,  -*  mav  be  com- 
puted. It  will  be  seen  that  as  d  decreases  C  increases,  and  as  the 
range  depends  directly  upon  the  value  of  C,  such  range  will  be 
greater  as  d  becomes  less.  Where  firing  is  more  or  less  continuous 
throughout  the  day  marked  changes  in  range  for  the  same  laying  are 
apt  to  be  noted,  but,  like  variations  due  to  muzzle  velocity,  the 
changes  are  corrected  in  the  bracketing  process  and  no  computation 
is  necessary  for  them  in  the  field. 

20.  AX  for  wind. — The  ninth  column  of  the  range  table  shows 
the  effect  of  a  10-mile  wind  blowing  up  or  down  the  range.     This 
column  is  based  on  the  assumption  that  the  wind  is  blowing  con- 
stantly at  the  assumed  rate. 


GUNNERY  AND  EXPLOSIVES.  23 

21.  Drift.  —  The  service  projectile  leaves  the  muzzle  of  the  gun 
with  a  velocity  in  the  direction  of  the  trajectory  and  a  motion  of  ro- 
tation about  its  longer  axis.     This  rotation  is  impressed  upon  the  pro- 
jectile during  its  interior  flight,  and  is  for  the  purpose  of  steadying 
or  stabilizing  its  subsequent  progress.     The  effect  of  the  resistance 
of  the  air  on  the  rotating  projectile  is  a  movement  of  the  projectile 
out  of  and  to  the  right  of  the  plane  of  fire.     This  departure,  Tcf  in 
figure  1,  is  called  drift. 

In  order  to  lay  for  direction,  the  amount  of  motion  of  the  projectile 
out  of  the  plane  of  fire  should  be  known.  This  information  is  tabu- 
lated in  the  tenth  and  eleventh  columns  of  the  range  table.  Ordi- 
narily the  deflection  is  not  greatly  affected  due  to  wind  and  drift, 
and  in  practice  the  amount  of  such  correction  is  estimated.  The 
empirical  rules  contained  in  Field  Artillery  Drill  Regulations  are 
sufficiently  accurate  for  all  practical  purposes. 

22.  Angle  of  fall.—  The  twelfth  and  thirteenth  columns  of  the 
range  table  contain  information  concerning  the  descending  branch 
of  the  trajectory.     The  value  of  this  information  will  become  appar- 
ent when  the  subject  of  shrapnel  fire  is  taken  up. 

23.  Time  of  flight.  —  The  fourteenth  column  of  the  range  table 
contains  the  times  of  flight  corresponding  to  the  tabulated  ranges. 

24.  Terminal  velocity.  —  The  fifteenth  column  of  the  range  table 
contains  the  terminal  velocities.     An  increased  velocity  of  about 
250  feet  is  imparted  to  the  shrapnel  balls  by  the  bursting  charge; 
hence  it  will  be  seen  that,  based  upon   a  killing  velocity  of  400 
foot-seconds  for  men  and  880  foot-seconds  for  horses,  the  terminal 
velocity  at  the  maximum  recorded  range  is  ample. 

25.  Maximum  ordinate.  —  The  last  column  contains  the  maxi- 
mum ordinate  corresponding  to  the  tabulated  range.     These  ordi- 
nates  have  been  computed  by  methods  set  forth  in  exterior  ballis- 
tics and  are  the  vertical  distances  from  the  horizontal  range  to  the 
summit  or  highest  point  of  the  trajectory.     A  convenient  approxi- 
mate formula  for  the  maximum  ordinate  is: 


in  which  h  is  the  maximum  ordinate  in  feet  and  t  the  corresponding 
time  of  flight  in  seconds.  The  range  "to  the  maximum  ordinate  is 
approximately  that  range  corresponding  to  an  angle  of  departure 
half  as  great.  For  instance,  the  angle  of  departure  corresponding 
to  a  range  of  6,500  yards  is  17°  12X6;  one-half  of  this  angle  is  8°  36X3 
which  corresponds  to  a  range  of  4,250  yards. 


24  GUNNERY  AND  EXPLOSIVES. 

26.  General  remarks. — As  previously  stated  in  this  chapter, 
in  the  field  reference  to  the  range  table  will  be  rare.  The  instru- 
ments of  precision,  without  which  the  battery  is  in  an  unequipped 
state,  are  themselves  constructed  in  such  manner  as  to  make  the 
use  of  the  range  table  in  the  field  almost  wholly  unnecessary.  These 
instruments  are  the  sights,  the  range  quadrant  and  the  fuse  setter, 
descriptions  of  all  of  which  may  be  found  in  the  handbook.  The 
gun  and  ammunition  will  respond,  within  reasonable  limits,  to  any 
changes  made  in  the  laying  for  range  and  direction;  the  time  burst 
of  the  fuse  may  be  varied  at  will,  hence  from  a  practical  viewpoint 
all  that  is  needed  in  the  field  is  a  firing  unit  properly  equipped, 
together  with  ample  ammunition  for  adjustment  of  fire  and  subse- 
quent fire  for  effect.  The  results  obtained  will  then  depend  upon 
the  handling  of  the  equipment  by  the  personnel. 

The  theoretical  study  of  the  range  tables  by  officers  is,  however, 
necessary  in  order  that  they  may  acquire  a  sound  understanding  of 
the  practical  uses  of  the  materiel  as  laid  down  in  the  Drill  Regula- 
tions, and  to  lead  to  progress  and  improvement  in  methods  and 
materiel. 


CHAPTER  IV. 

AMMUNITION    FOR    THE    LIGHT  FIELD    <3UN. 

27.  Classification. — The  ammunition  available  for  use  with  the 
3-inch  field  guns  at  present  is  of  three  kinds,  i.  e.,  common  shrapnel, 
high-explosive  shell,  and  high-explosive  shrapnel.     Shrapnel  is  the 
principal  projectile  of  our  present  field  artillery  and  in  the  form  of 
high-explosive  shrapnel  will  become  the  only  projectile  within  a 
short  time. 

28.  Common    shrapnel. — The    construction    of    the    common 
shrapnel  is  described  in  the  handbook.     An  examination  of   the 
design  will  show  that  the   modern   shrapnel  is  a  projectile  which 
carries  a  number  of  bullets  to  a  distance  from  the  gun,  where  they 
are  discharged  with  killing  energy  over  an  extended  area.     The 
shrapnel  is  made  of  an  exceptionally  strong  drawn  steel  case,  which 
remains  intact  upon  the  explosion  of  the  bursting  charge.     Formerly 
the  shrapnel  case  ruptured  at  the  instant  of  time  burst,  hence  failed 
to  give  the  accurate  spread  of  bullets  so  easily  noticeable  in  the  more 
recent  product.     For  the  purpose  of  facilitating  observation  of  fire 
a  portion  of  the  matrix  surrounding  the  shrapnel  balls  is  of  smoke- 
producing   material.     The  advantage   of  having  a  point  in    the 
shrapnel's  trajectory  made  visible,  as  well  as  being  able  to  observe 
some  of  the  dust  thrown  up  by  the  balls  upon  impact,  is  obvious. 

The  fuse  used  in  the  shrapnel  is  the  F.  A.  21-second  combination 
fuse,  model  of  1907,  and  is  arranged  so  that  if  the  projectile  fails  to 
burst  in  flight  it  will  burst  upon  graze  or  soon  after.  The  fuse  may 
be  set  at  zero,  whereupon  the  shrapnel  will  burst  at  about  20  feet 
from  the  muzzle  of  the  gun.  The  common  shrapnel  is  essentially 
a  projectile  for  attacking  personnel  and  has  little  or  no  effect  against 
walls  or  even  light  entrenchments.  Used  in  an  attack  of  a  field  work 
of  even  temporary  type,  its  function  is  to  keep  down  the  defenders 
until  our  infantry  can  advance  sufficiently  to  warrant  a  rush  on  the 
position. 

NOTE.— As  a  matter  of  interest  to  field  artillery  officers  and  to  officers  of  infantry, 
and  particularly  for  trie  benefit  of  those  officers  who  recall  the  almost  hopeless  irregu- 
larity of  action  of  the  old  type  of  fuse,  the  following  results  of  firing  with  the  model  1907 
fuse  are  quoted: 

EEGIMENTAL  PROBLEM. 

On  November  8,  1910,  the  regimental  commander  of  the  Sixth  Field  Artillery 
conducted  the  fire  of  his  regiment  against  a  line  of  trenches  represented  by  490  kneeling 

25 


26  GUNNERY  AND  EXPLOSIVES. 

figures  at  a  range  of  2,200  yards.  It  was  supposed  that  friendly  infantry  was  advanc- 
ing against  the  trenches,  hence  there  were  three  lines  of  standing  and  kneeling  figures 
at  100  yards,  200  yards,  and  300  yards  from  the  enemy's  trenches.  There  were  320 
figures  in  the  friendly  lines. 

The  ammunition  used  was  common  shrapnel,  fused  with  the  model  of  1907  fuse.  In 
the  enemy's  trenches  358  out  of  490  figures  were  hit— an  average  of  73  per  cent. 
In  the  advancing  infantry  only  3  figures  were  hit— all  on  left  of  line  nearest  target. 
In  all  there  were  140  rounds  fired. 

29.  High-explosive  shell. — Due  to  the  fact  that  common  shrapnel 
was  without  sufficient  effect  when  used  against  walls,  trenches,  light 
cover,  and  the  enemy's  materiel,  it  became  necessary  to  adopt  a 
high-explosive  shell.     The  shell  bursts  upon  impact   against  the 
obstacle  or  after  having  penetrated.     In  theory  the  shell  is  merely 
the  vehicle  for  the  transportation  of  some  high  explosive  to  be  made 
effective  upon  impact.     As  a  matter  of  fact  the  quantity  of  high 
explosive  in  a  3-inch  shell  is  so  small  that  the  effect  of  detonation  is 
much  less  extensive  than  might  be  supposed.     A  typical  use  of 
high-explosive  shell  is  found  in  its  employment  against  the  guns  of 
an  opponent's  battery  which  has  been  silenced  temporarily  as  the 
result  of  overpowering  shrapnel  fire. 

High-explosive  shell  may  be  used  to  demolish  overhead  and 
head  cover  as  a  preparation  for  subsequent  shrapnel  fire. 

30.  High-explosive  shrapnel. — Notwithstanding  the  fact  that 
shrapnel  is  the  principal  projectile  for  the  field  artillery,  it  will  be 
seen  that  certain  functions  of  the  high-explosive  shell  are  also  neces- 
sary.   The  high-explosive  shrapnel  has  been  designed  to  embody  as 
fully  as  possible  'the  good  features  of  the  common  shrapnel  and  the 
high -explosive  shell.     The  high -explosive   shrapnel,  without  fuse, 
is  practically  the  same  as  the  common  shrapnel,  so  far  as  its  construc- 
tion goes.     Actually  the  only  essential  difference  is  the  substitution 
of  an  active  for  an  inert  matrix.     The  matrix  surrounding  the  balls 
in  a  common  shrapnel  is  resin  and  mono-nitro-naphthalene ;  in  the 
high -explosive  shrapnel  the  matrix  is  tri-nitro-  toluol,  a  high  explosive. 

The  fuse  of  the  high-explosive  shrapnel,  in  so  far  as  the  time  action 
is  regulated,  is  the  same  as  the  present  field  artillery  21-second  com- 
bination fuse,  model  1907.     The  essential  difference  is  that  for  the 
percussion-ignition  effect  in  the  common  shrapnel  fuse  a  percussion- 
detonation  effect  has  been  substituted.    The  difference  between  the 
two  effects  will  be  considered  in  a  chapter  on  explosives. 
The  high  explosive  shrapnel  affords  the  following  advantages: 
(a)  It  is  a  single-type  projectile,  hence  obviates  the  difficulty  of 
supplying  two  forma  of  ammunition.     Heretofore  much  discussion 


GUNNERY  AND  EXPLOSIVES.  27 

has  taken  place  regarding  the  proportion  of  shell  to  shrapnel.     The 
problem,  though  indeterminate  when  two  forms  of  projectiles  are 


explosive  head  should  be  effective  against  the  carriages  of  opposing 
artillery.  Also  it  should  facilitate  observation  of  fire. 

(c)  High-explosive  shrapnel  has  considerable  shrapnel  effect  when 
bursting  on  impact,  whereas  common  shrapnel  is  practically  harm- 
less unless  striking  on  hard  ground. 

It  should  be  understood  that  the  high-explosive  shrapnel  is  a 
compromise  projectile,  justified  unquestionably  by  the  resulting 
simplification  of  ammunition  supply.  The  shell  effect  of  the  single- 
type  projectile  is  slightly  inferior  to  that  of  the  high-explosive  shell, 
and  the  number  of  balls  contained  in  its  case  is  fewer  than  in  the 
common  shrapnel. 


CHAPTER  V. 

CALCULATION    OF   THE    ELEMENTS    OF   FIRE. 

31.  General  considerations. — Field  Artillery  Drill  Regulations 
contain  sufficient  information  to  enable  a  commander  of  a  field 
artillery  unit  to  direct  the  fire  of  his  unit  upon  any  target  assigned 
to  him.    This  part  of  the  regulations  should  be  studied  carefully, 
as  it  contains  the  rules  upon  which  the  mastery  of  the  commander 
over  his  plant  is  based.    The  materiel  has  been  designed  for  rapid, 
accurate  work;  it  is  supposed  that  the  personnel  have  been  trained 
properly;  it  now  becomes  the  duty  of  the  individual  in  control  of 
this  plant  to  equip  himself  with  the  power  to  use  it  rapidly  and 
efficiently. 

32.  Preliminary  computation. — For  direct  laying,  few,  if  any, 
computations  are  necessary.     The  aiming  point  is  the  target  itself 
and  the  deflection  set  off  on  the  sight  compensates  for  drift  and  wind. 
No  correction  for  angle  of  sight  is  necessary,  due  to  the  fact  that  the 
range  is  set  off  on  the  rear  sight  shank,  after  which  the  line  of  sight 
is  directed  upon  the  target. 

When  indirect  laying  is  employed  it  becomes  necessary  to  deter- 
mine the  horizontal  angle  between  the  axis  of  each  piece,  properly 
directed  upon  its  target,  and  the  line  joining  each  panoramic  sight 
and  the  selected  aiming  point.  The  angle  of  site  from  gun  to  target 
must  be  determined  and  the  guns  must  be  located  in  such  manner 
that  their  fire  will  clear  the  mask  and  otherwise  conform  to  the  nature 
of  the  particular  problem.  Firing  data  are  determined  at  the  observ- 
ing station  and  there  transformed  for  use  at  the  guns. 

33.  Deflection  of  any  piece.— The  solution  of  this  problem  has 
for  its  aim  the  determination  of  the  horizontal  angle  in  mils  between 
the  line  of  sight  and  the  axis  of  the  piece,  so  that  the  fire  of  this  piece 
may  be  toward  and  in  the  direction  of  the  assigned  target.     In 

28 


GUNNERY  AND  EXPLOSIVES. 


the  general  problem  any 
position  may  be  chosen 
for  the  gun,  aiming 
point,  target,  and  observ- 
ing station.  The  angular 
quantities  entering  the 
solution  are  obtained  at 
the  observing  station  by 
means  of  the  battery  com- 
mander's telescope,  the 
battery  commander's 
ruler,  orbyhandbreadths; 
linear  elements  entering 
the  solution  are  measured 
or  estimated.  In  the 
usual  case  the  deflection 
of  the  right  piece  is  de- 
tennined^and  a  deflection 
difference  calculated, 
which,  if  applied  in  arith- 
metrical  progression  to 
the  deflection  of  the  right 
piece,  gives  the  proper 
.deflection  for  the  piece 
considered . 

34.  Deflection  of  the 
right  piece.— In  figure  3, 
T  is  the  position  of  the 
target;  G  the  position  of 
the  gun;  B  and  P  the 
positions  of  the  B.C.  tel- 
escope and  aiming  point, 
respectively.  T  repre- 
sents also  the  angle  BTG; 
P  the  angle  BPG;  B  the 
angle  PBT;  A  the  angle 
PGT,  which  is  the  sum  of 
the  angles  a  and  d. 


30  GUNNERY  AND  EXPLOSIVES. 

Based  upon  the  fact  that  the  sum  of  the  interior  angles  of  a  triangle 
equals  180°  and  that  the  sum  of  the  angles  about  a  point  equals  360°, 
the  following  equations  may  be  written: 


by  addition 

also 

by  subtraction 

hence 

a+c/=A=B-P-T=B+(-P)-T 

in  which  A  is  the  deflection  required,  B  is  the  measured  deflection 
at  the  B.  C.  station  from  aiming  point  to  target;  it  being  impossible 
to  measure  T  and  P,  these  angles  must  be  computed  by  trigono- 
metrical methods  or  by  approximate  methods  to  be  explained. 
From  trigonometry 

Sin  P_Sin  c 
BG       PG 
and 

Sin  T_Sin  b 
BG        PG 

TG  is  the  range  from  gun  to  target. 

PG  is  the  distance  from  gun  to  aiming  point,  and  BG  is  the  distance 
from  gun  to  B.  C.  station,  which  distances  must  be  accurately  known, 
if  the  deflection  desired  is  to  be  accurately  determined. 

Taking  another  case  and  retaining  the  nomenclature  in  figure  3, 
refer  to  figure  4,  in  which  — 


<M-c+P=180° 

hence 

a-f  6=180°  -T 
d+c=18V°-P 

but 


therefore 


GUNNERY  AND  EXPLOSIVES. 


31 


substituting 

B+180-T=A-f-180--P 
solving 

A=B+(+P)-T 

from  which  it  is  seen  that  the  required  deflection  of  the  right  piece 
can  always  be  expressed  in  terms  of  B,  P,  and  T,  and  that  P  is  posi- 
tive when  the  aim- 
ing point  is  in  front 
of  the  line  BG,  and 
negative  when  in 
rear. 

In  theory  the 
deflection  of  any 
piece  may  be  de- 
termined as  shown 
above  for  the  right 
piece.  The  meas- 
ured angle  B  is 
constant,  but  P 
.and  T  vary  with 
BG,  which  is  the 
distance  from  the 
observing  station 
to  the  gun  consid- 
ered. In  practice 
the  application  of 
accurate  trigono- 
metric methods  is 
not  warranted,  as 
exceptionally  close 
approxima  tions 
may  be  made 
quickly.  The 
manner  of  making 
such  approxima- 
tions will  be  con- 
sidered under  the 
t  h  e  o  ry  of  paral- 
laxes. 


32 


GUNNERY  AND  EXPLOSIVES. 


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35.  Deflection  differences. — If  the  guns 
of  a  battery  at  GT  G4  in  figure  5  be  accurately 
laid  for  converging  fire  upon  a  target  ^  and 
the  panoramic  sights  be  then  turned  upon  a 
common  aiming  point  P,  the  sight  readings 
will  be  found  to  vary  from  GA  to  G4  by  differ- 
ences which  are  for  all  practical  purposes 
equal  from  gun  to  gun  throughout  the  bat- 
tery. It  is  evident  from  the  figure  that  if  the 
azimuth  or  deflection  for  the  right  piece  be 
known,  that  for  the  second  piece  may  be  ob- 
tained by  applying  the  common  difference 
to  the  sight  reading  of  the  right  piece.  In 
a  similar  manner  the  sight  settings  for  the 
third  and  fourth  pieces  may  be  found.  This 
common  difference  is  called  the  convergence 
difference. 

If  now  it  be  desired  to  lay  the  guns  so  as 
to  distribute  the  fire  over  the  entire  front  of 
the  target  EF,  ^  being  the  particular  target 
of  the  right  piece  and  £4  that  of  the  left  piece, 
it  will  be  seen  that  the  readings  of  the  sight 
at  G2  must  be  increased  by  the  angle  ^G^ 
expressed  in  mils;  that  of  G3  must  be  in- 
creased by  twice  as  much,  and  that  of  G4  by 
three  times  as  much .  There  is  consequently 
a  second  common  difference  which,  added 
to  the  sight  settings  for  converging  fire,  will 
give  the  correct  settings  for  distributed  fire. 
This  common  difference  is  called  the  distri- 
bution difference. 

The  algebraic  sum  of  the  two  differences 
is  called  the  deflection  difference.  In  the  case 
of  converging  fire,  the  distribution  differ- 
ence is  zero  and  the  deflection  difference  is 
the  same  as  the  convergence  difference;  in 
the  case  of  parallel  fire,  the  distribution 
difference  added  is  equal  to  the  parallax  of 
the  target,  and  the  deflection  difference 
therefore  becomes  equal  to  the  parallax  of 
the  aiming  point. 


GUNNERY  AND  EXPLOSIVES. 


33 


To  lay  the  guns  upon  their  appropriate  targets  in  indirect  laying, 
it  is  then  necessary  to  determine,  first,  the  deflection  of  the  right 
piece  and,  second,  the  deflection  difference. 

36.  Parallax  of  a  point.— In  practice  the  parallax  of  a  point 
is  taken  to  be  the  angle,  expressed  in  mils,  subtended  at  the  assumed 
point  by  one  platoon  front  (20  yards)  at  the  position  of  the  observer. 

Thus  if  G!,  G2,  figure  6,  repre- 
sents a  platoon  front,  the  paral- 
lax of  T  is  the  angle  GXTG2  in 
mils.  The  parallax  of  P  is  the 
angle  GiPG2.  Applying  the  rule 
A=B  +  (P-T)  to  this  case  A 
becomes  A2  and  B  becomes  A1? 
hence  A2— A^P— T,  in  which 
P  is  positive  when  the  aiming 
point  is  in  front  of  the  line  of 
guns  and  negative  when  in  rear. 
It  should  be  noted  that  in  this 
case  A!  is  the  deflection  of  the 
right  piece  and  A2  is  the  deflection 
of  the  second  piece.  A2— A!  is 
therefore  the  convergence  differ- 
ence, usually  represented  by  CD. 

Therefore  to  determine  the 
convergence  difference,  knowing 
the  parallax  of  the  aiming  point 
and  that  of  the  target:  Subtract 
algebraically  the  parallax  of  the 
target  from  the  parallax  of  the 
aiming  point,  giving  to  the  latter 
the  negative  sign  when  the  aiming 
point  is  in  rear  of  the  gun;  the  re- 
sult, positive  or  negative,  is  the  cori- 
vergence  difference.  Qi  ~£r 

Without  entering  further  into 

the  subject  it  is  believed  that  the  reasons  for  the  rules  set  forth 
in  the  Drill  Regulations  for  the  determination  of  the  deflection 
difference  will  be  apparent. 

The  rules  give  a  ready  means  of  obtaining  the  deflection  difference 
when  the  parallaxes  of  the  target  and  aiming  points  are  known.     To 
determine  these  parallaxes  the  range  and  the  distance  to  aiming 
point  should  be  determined, 
'—ll — 3 


GUNNERY  AND  EXPLOSIVES. 


37.  Application  of  rules  for  determining  deflection  differ- 
ences.— The  parallax  of  a  point  directly  in  rear  of  a  firing  unit 
at  normal  intervals  is  20  divided  by  range  to  point  in  thousands  of 
yards;  if,  however,  the  point  is  taken  on  the  extension  of  the  line 
of  guns,  the  parallax  becomes  zero.  In  figure  7,  GxG2  is  one  platoon 
front  and  Px,  Px/,  Px//  are  different  positions  of  the  aiming  point. 


(ry.7) 


It  will  be  seen  that  the  angle  G2PGj  has  its  maximum  value  when 
the  aiming  point  is  directly  in  rear  and  that  the  angle  in  question 
diminishes  in  value  until  P  coincides  with  P/x/,  where  the  paral- 
lax is  zero.  When  the  line  from  aiming  point  to  any  piece  is  con- 
siderably oblique  to  the  line  of  guns,  such  obliquity  must  be  con- 
sidered in  arriving  at  the  proper  value  for  the  parallax.  By  means 
of  the  parallax  table  on  the  B.  C.  ruler  can  be  found  the  parallax 


GUNNERY  AND  EXPLOSIVES.  35 

of  a  target  or  aiming  point  situated  in  any  direction  with  reference 
to  the  front  of  the  firing  unit.     The  parallax  of  P  above  varies  from 

20 

X  to   zero,   hence  for  distant  aiming  points  no  great  error  will 
1000 
be  made  in  neglecting.  corrections  for  obliquity. 

38.  Application  of  rule  for  determining  deflection  of  right 
piece.  —  If  the  observing  station,  B,  figure  5,  on  the  right  flank 
of  the  firing  unit,  is  but  one  platoon  front  away,  the  deflection  of 
the  right  piece  is  obtained  by  applying  the  convergence  difference 
to  the  measured  deflection  at  the  observing  station.  If  the  observ- 
ing station  is  n  platoon  fronts  away,  n  times  the  convergence  differ- 
ence must  be  applied  to  the  measured  deflection  PB£,  or 


The  essential  signs  of  both  n  and  CD  must  be  considered,  n  being 
positive  when  the  B.  C.  telescope  is  to  the  right  of  the  firing  unit 
and  negative  when  it  is  to  the  left. 

As  n  increases  it  is  necessary  to  determine  with  greater  accuracy 
the  value  of  the  convergence  difference. 

If  the  observation  station  is  not  exactly  on  the  prolongation  of  the 
line  of  guns,  but  is  near  it,  the  deflections  may  be  determined  prac- 
tically as  explained  in  the  case  when  the  B.C.  telescope  is  on  the 
prolongation  of  the  line  of  guns,  except  that  instead  of  measuring 
the  distance  from  observing  station  to  right  piece  to  determine  n, 
the-  distance-  from  observing  station  to  the  line  of  fire  G^  is  measured 
on  a  line  parallel  to  the  front  of  the  firing  unit. 

The  solution  of  a  prDblem  will  illustrate  the  application  of  the 
parallax  method. 
Measured  deflection: 

B=4,165 

P=  —  2.2  (obliquity  considered  corresponding  to    measured 
deflection)  . 


T_    20     7 

~  2^? 

Deflection  of  right  piece=PG1£1=4,165+18  (-2.2-7) 

=4,165-166 
=3,999 


36 


GUNNERY  AND  EXPLOSIVES. 


GUNNERY  AND  EXPLOSIVES.  37 


For  converging  fire 

DD=CD=-10 
hence  PG^-3,989 


For  distributed  fire 

Deflection  difference  =-2.2  -7+^. 

-X. 

in  which  F  is  front  of  targets  in  mils  and  X  equais  number  of  guns 
to  which  target  is  assigned. 
Suppose  F=150  mils 
X=4 

TT 

then  =37 


DD  =  -2.2-7+37  = 

For  parallel  fire  : 

In  order  to  cause  the  pieces  to  be  directed  on  the  opposing  parts 
of  their  targets,  deflection  difference^  parallax  of  aiming  point  = 
—2.2,  since, 


F    80 


in  which  F  is  front  of  target  in  mils  and  X  equals  number  of  guns 
firing. 


CHAPTER  VI. 

RAPID    CALCULATION    OF  THE    ELEMENTS    OP  THE    TRAJECTORY. 

39.  General  considerations.  —  As  is  the  case  with  other  pro- 
fessions the  practice  of  which  is  based  upon  the  intelligent  appli- 
cation of  natural  laws,  field  artillery  has  its  empirical  rules.     Such 
rules  are  more  or  less  closely  in  accord  with  mathematical  facts,  the 
departure  from  such  facts  being  in  the  form  of  close  approximations 
easily  remembered  and  quickly  applied.     All  the  elements  of  the 
trajectory  in  air  may  be  computed  with  any  desired  degree  of  accu- 
racy, but  such  computations  can  not  be  made  quickly  even  under 
the  most  favorable  conditions.     Due  to  certain  interesting  relations 
between  various  elements  of  the  trajectory,  approximations  suffi- 
ciently close  for  practical   purposes   may  be  carried  in  the  head 
without  the  necessity  of  using  range  tables  or  logarithms. 

40.  Units  of  measure.  —  The  yard  is  the  usual  unit  of  distance. 
The  unit  angle  is  the  mil. 

The  true  mil  is  a  thousandth  part  of  a  radian,  or  practically 


,  T7 

part  of  a  right  angle  ;  the  mil  adopted  is  T^TT  Par^  °f  a  right  angle 
and  is  smaller  than  the  true  mil  by  approximately  4  seconds  of  arc. 

Based  upon  the  assumption  that  6,400  mils  equals  360  degrees,  or 
21,600  minutes,  degrees  may  be  converted  into  mils  by  first  reducing 
the  degrees  to  minutes  and  then  multiplying  by  0.3. 

Example:  The  angle  of  departure  5°  12',  corresponding  to  a  hori- 
zontal range  of  3,000  yards,  equals  312  minutes,  or  93.6  mils.  Actu- 
ally, the  angle  in  mils  should  be  92.4,  which  does  not  vary  greatly 
from  that  given  by  the  approximate  method  . 

The  converse  of  the  above  rule  is  true,  and  mils  may  be  trans- 
formed into  minutes  by  dividing  by  0.3. 

41.  Angles  of  departure.  —  Denote  by  K  any  tabular  range  in 
thousands  of  yards.  If  <£  is  the  angle  of  departure  in  mils  corre- 
sponding to  a  range  less  by  a  hundred  yards,  then  ^  corresponding 
to  the  range  K  will  be  equal  to  (j>  +  K  +  1.4  in  mils,  or,  the  incre- 
ment of  the  angle  of  departure  corresponding  to  an  increase  in  range  of 
100  yards  is  equal  to  K  +  1.4  mils. 


38 


GUNNERY  AND  EXPLOSIVES.  39 

Example:  The  angle  of  departure  for  range  3,000  is  92.4  mils. 
For  3,100  yards  K  =  3.1,  hence  increment  <£  equals  3.1  +  1.4  or 
4.5  mils,  which  added  to  92.4  gives  96.9  mils,  differing  by  only  -£$ 
of  a  mil  from  the  tabular  angle  of  departure. 

Example:  <£  for  4,800  yards  is  186  mils;  K  for  4,900  equals  4.9; 
cf>  for  4,900  yards  is  192.3  mils. 

The  above  rule  may  be  written  in  a  more  general  form,  as  follows: 
The  increment  of  the  angle  of  departure  corresponding  to '  an  increase 
in  range  ofnlOO  yards  is  equal  to  n(^T1+  1.4)  mils.  Kx  is  the  average 
value  in  thousands  of  yards  of  the  two  ranges  considered. 

Example:  The  angle  of  departure  for  range  1,000  is  21  mils;  for 

6,500  yards  K^   '  ^     =3.75;  55X3.75  equals  206. 25;  55X1.4  equals 

77;  </>  for  6,500  equals  206  +  77  +  21  =  304  mils  (tabular  value  is 
305.8). 

The  above  rules  assume  that  the  angle  of  departure  corresponding 
to  some  range  has  been  committed  to  memory.  This  is  not  neces- 
sary, as  the  angle  of  departure  corresponding  to  any  range  may  be 
computed  by  means  of  the  following  formula: 

<£  in  mils  =  5K(K+3) 

Example:  Let  it  be  required  to  compute  the  angle  of  departure 
corresponding  to  a  range  of  4,000  yards.  K  =  4;  20(4  -(-  3)  =  140  mils. 

42.  Range  for  any  assumed  angle  of  departure. — Take  the 
equation 


Solve  for  K, 
Completing  square 
Extracting  root, 


K2+3K+|=|+f 


40  GUNNERY  AND  EXPLOSIVES. 

Transposing  and  simplifying 


Example:  Given  <£=114  mils;  required  the  corresponding  range. 


K-    /114+11     15-35 

K-^/— ^_ 


The  range  is  therefore  3,500  yards. 
Suppose  </>=306  mils. 


K=-./—-— 1.5=6.5  (very  closely), 

or  the  range  is  6,500  yards. 

43.  Angle  of  fall. — The  angle  of  fall,  in  mils,  is  approximately 
one  and  a  half  times  the  angle  of  departure.  At  a  range  of  6,500  yards 
the  angle  of  fall  computed  by  the  approximate  method  would  be 
about  10  mils  too  small;  at  short  and  mid  ranges  the  variation  is 
negligible. 

It  will  be  seen  that  the  formulas  for  ascertaining  the  angle  of 
departure  corresponding  to  an  assumed  range  apply  to  angles  of 
fall  by  the  introduction  of  the  factor  f  in  the  second  terms. 

For  instance, 


becomes 

ft>=7..5K(K+3). 

44.  Time  of  flight.  —  An  approximate  equation  for  obtaining  the 
value  of  the  time  of  flight  may  be  written  as  follows: 

/0+K     K»)\      t     /K    K»\     0     K/l 

=    ~ 


in  which  </>  is  the  angle  of  departure  in  mils. 

From  an  examination  of  this  equation  it  will  be  seen  that  for  short 
ranges  a  close  approximation  to  the  time  of  flight  will  result  from 
taking  one-tenth  of  the  corresponding  angle  of  departure  in  mils. 


GUNNERY  AND  EXPLOSIVES.  41 

Substituting  in  the  equation  under  consideration  the  value  of  $  in 
terms  of  the  range,  or,  ^>=5K(K-f-3),  we  find : 

T=:r~(3K-f-16),  a  very  simple  formula  and  dependent  upon  the 

range  alone. 

Thus  for                                                                                           Tabular  values. 
1,000  yards  T=1.9 2.  07 


2,000  yards! 
3,000  yards' 
4,000  yards! 
5,000  yards, 
6,000  yards! 


T=4.4 4.  75 

T=7.5 7.83 

T=  11.20 11.  25 

T=15.5 15.  12 

T=20.4 19.  36 


The  formula  is  sufficiently  accurate  at  all  ranges,  and  particularly 
so  from  2,500  to  5,000  yards. 

45.  Maximum  ordinate. — The  maximum  ordinate  is  equal  in 
feet  approximately  to  four  times  the  square  of  the  time  of  flight  in 
seconds.     It  is  at  a  distance  from  the  origin  equal  to  approximately 
three-fifths  of  the  range,  or  the  range  to  the  foot  of  any  maximum 
ordinate  is  equal  to  that  resulting  from  one-half  the  angle  of  departure. 

Example:  For  a  range  of  4,200  yards  the  time  of  flight  is  11.99 
(say  12)  seconds;  4X122=576  feet  (tabular  value  610);  the  distance 
to  maximum  ordinate  is  three-fifths  of  4,200,  or  2,520  yards;  the 
angle  of  departure  for  4,200  yards  is  151.4  mils,  one-half  of  which — 
75.7  mils — corresponds  to  a  range  of  2,600  yards. 

46.  Firing  over  a  mask. — In  the  selection  of  concealed  positions 
it  is  important  to  so  locate  the  guns  that  the  trajectories  may  clear 
the  mask.     For  the  proper  solution  of  the  problem  a  knowledge  of 
the  height  of  the  trajectory  above  the  line  of  sight  IF»  necessary. 

For  cases  in  which  the  height  of  the  mask  in  yards  is  known,  Gen. 
Percin,  of  the  French  Artillery ,  has  deduced  a  simple  rule  of  approxi- 
mation. For  the  actual  trajectory  he  has  substituted  a  parabola 
passing  through  the  origin  and  the  point  of  fall,  whose  ordinates  at 
all  points  of  the  range  are  inferior  to  the  ordinates  of  the  real  tra- 
jectory. The  equation  of  the  Percin  parabola  is 

4y=x(R-x) 
in  which 

y  is  the  ordinate  in  yards  corresponding  to  any  point  x. 

x  is  in  the  general  sense  any  abscissa;  in  the  special  sense  it 

is  the  distance  from  gun  to  mask  in  hundreds  of  yards. 
R  is  the  entire  range  from  gun  to  object  in  hundreds  of  yards. 


42  GUNNERY  AND  EXPLOSIVES. 

Solving  for  x, 


from  which  it  is  seen  that,  under  the  rule,  a  projectile  will  clear  the 
mask  when  fired  at  a  distance  from  the  mask  equal  to  four  times  the 
height  of  the  mask  in  yards,  divided  by  the  range  from  mask  to 
object  in  hundreds  of  yards. 

Example:    The  range  from  mask  to  target  is  4,000  yards;  height 
of  mask  20  yards. 


z=200  yards. 

At  200  yards  the  angle  of  site  of  the  mask  is  100  mils;  the  angle  of 
departure  corresponding  to  range  of  4,200  yards  is  151.4  mils,  hence 
it  will  be  seen  that  the  rule  gives  a  large  factor  of  safety  for  hori- 
zontal ranges.  Even  for  an  angle  of  site  of  target  as  low  as  250  the 
projectiles  in  this  case  would  clear  the  mask. 

Let  S==  angle  of  site  of  mask 

y 

then    S=T=10^ 
10         X 

y=^ 

x     10 
from  the  equation  of  the  parabola  above 

y-=\  (R-x) 
or 

|j=i  (R-x) 

or 

S=2'.5  (R-z) 

_.om  which  it  is  seen  that  the  trajectory  will  clear  if  the  guns  are 
placed  at  a  distance  from  the  mask  such  that  the  angle  of  site  of  the 


GUNNERY  AND  EXPLOSIVES.  43 

mask  from  the  gun,  in  mils,  is  equal  to  or  less  than  two  and  one-half 
times  the  distance  from  mask  to  target  in  hundreds  of  yards. 

In  the  formula  just  considered  the  distance  from  mask  to  target 
has  been  considered,  no  allowance  having  been  made  for  approach 
of  target.  If  it  is  desired  to  limit  the  dead  space  to  a  definite  dis- 
tance this  distance  in  hundreds  of  yards  should  be  chosen,  instead 
of  the  range  from  mask  to  target.  Gen.  Tariel,  also  of  the  French 
Army,  has  written  a  formula  in  which  he  considers  the  necessity 
for  observation  of  the  ground  in  front  of  the  target.  In  his  formula 

S=30(K-1) 

Example:  Let  the  range  be  2,000  yards,  then  S=30  mils=  mini- 
mum angle  of  site  of  mask  from  position  of  guns;  30  mils  corresponds 
to  the  angle  of  departure  for  a  range  of  1,350  yards,  hence  there  will 
be  a  margin  of  fire  of  650  yards. 

In  the  discussion  contained  in  this  paragraph  it  has  been  assumed 
that  the  guns  and  target  are  on  the  same  horizontal  plane.  If  such 
is  not  the  case  the  angle  of  site  of  the  target  should  be  considered. 

Percin's  formula  becomes 


S=2.5  (R-aO  +  (e 
TarieFs  formuia  becomes 

S=30  (K-l)+0-300) 

47.  Height  of  trajectory  at  any  distance  from  origin.  —  For 

flat  trajectories,  or  in  other  words  whenever  the  principle  of  the 
rigidity  of  the  trajectory  applies,  the  relation  between  an  abscissa 
and  its  corresponding  ordinate  may  be  written  as  follows: 

2/=z  W>k-<£x) 

<£k  is  the  angle  in  mils  corresponding  to  the  entire  range. 

<j)^  is  the  angle  in  mils  corresponding  to  the  abscissa  x. 

y  is  height  of  ordinate  in  yards. 

x  is  the  abscissa  in  thousands  of  yards. 

From  the  equation  0  =5K(K+3) 
We  may  write  <£k=5K(K-}-3) 


44  GUNNERY  AND  EXPLOSIVES. 

Substituting  these  values  on  the  above  equation, 


we  have  an  equation  by  which  the  trajectory  corresponding  to  any 
range  may  be  constructed.     The  time  of  flight  may  be  found  from 

T=~(3K+16) 

For  the  angle  of  fall, 

o>=7.5K(K+3) 

The  student  should  bear  in  mind  that  the  above  formulas  are 
closely  approximate  only;  that  accuracy  resulting  from  the  applica- 
tion of  correct  ballistic  formulas  has  been  somewhat  sacrificed  in  the 
desire  for  simplicity  and  rapidity  of  computation  .  For  practical  pur- 
poses the  field  artilleryman  requires  no  more  accurate  methods  than 
the  ones  laid  down  in  this  chapter;  as  a  matter  of  interest,  however, 
he  is  referred  to  the  well-known  texts  dealing  with  the  subject  of 
exterior  ballistics. 

The  approximate  methods  set  forth  in  this  chapter  may  be  applied 
to  any  gun,  with  obvious  changes  in  the  constants.  For  instance, 
referring  to  the  range  table  for  2.95-inch  mountain  gun  (Yickers- 
Maxim),  12^-pound  projectile,  muzzle  velocity  920  feet  per  second, 
it  will  be  seen  that 

(angle  of  elevation)=8K(K+6) 
(time  of  flight)         = 


CHAPTER  VII. 

ACCURACY   OF   FIRE    AND    CAUSES    AFFECTING   IT. 

48.  Causes  affecting  accuracy. — There  are  two  principal  causes 
affecting  the  accuracy  of  field  gun  fire: 

First.  Errors  committed  by  the  personnel  charged  with  the  various 
incidents  of  fire. 

Second.  Irregularities  in  the  materiel  supplied  by  the  Ordnance 
Department. 

49.  Errors  committed  by  the  personnel. — In  order  that  the 
projectile  from  any  gun  may  hit  the  target  the  gun  must  be  fired  at  a 
certain  angle  of  departure,  depending  upon  the  range  and  upon  the 
relative  level  of  the  gun  and  the  target,  and  must  be  given  such  direc- 
tion to  the  right  or  left  of  the  target  as  to  neutralize  the  deviation 
of  the  shot  from  the  plane  of  fire  due  to  the  drift  and  wind.     In 
shrapnel  fire  the  fuse  must  be  set  to  function  at  the  proper  height 
and  at  the  proper  distance  in  front  of  the  target. 

Whether  the  laying  be  direct  or  indirect,  the  accuracy  of  fire 
depends  upon  the  correct  manipulation  of  the  instruments  for  laying 
and  fuse  setting.  The  battery  commander  is  responsible  for  the 
correct  adjustment  of  his  instruments  before  firing;  and  during  target 
practice  or  combat  the  platoon  commanders  and  chiefs  of  sections 
supervise  the  service  of  their  guns,  the  latter  watching  particularly 
to  see  that  sights,  quadrants,  and  fuses  are  properly  set.  It  must 
be  understood  that  before  the  broader  moves  in  the  artillery  game 
may  be  played  with  confidence,  and  before  the  commander  can 
utilize  the  wonderful  flexibility  of  his  fire,  he  must  train  his  organ- 
ization in  the  manipulation  of  the  few  instruments  of  precision  with 
which  the  guns  are  equipped.  When  the  machine  is  perfect  within 
itself,  its  commander  will  realize  his  reward  in  the  possession  of  a 
fighting  unit  of  enormous  power,  susceptible  of  accurate  and  flexible 
direction. 

Based  upon  the  analysis  of  many  rounds  of  the  3-inch  shrapnel 
ammunition,  fired  at  proving  grounds,  we  may  safely  conclude  that 
where  the  gun  has  been  accurately  laid  in  elevation  and  for  direction 

45 


46  GUNNERY  AND  EXPLOSIVES. 

range  errors  will  be  negligibly  small.  This  refers  particularly  to 
bursts  upon  impact  with  the  ground  and  only  in  a  general  way  to  air 
bursts,  which  latter  action  does  not  depend  solely  upon  the  proper 
laying  and  fuse  setting. 

50.  Irregularities  in  materiel. — The  gun  and  ammunition  are 
subject  to  the  usual  errors  found  in  manufactured  products.  Com- 
pared with  commercial  articles^the  accuracy  and  regularity  of  their 
construction  is  remarkably  high,  due  principally  to  the  well-drawn 
specifications  furnished  by  the  Government  and  to  the  careful 
inspection  of  all  material  and  the  manner  of  converting  it  into  war 
supplies. 

Any  error  existing  in  a  new  field  gun  is  negligible.  A  gun  which 
has  had  a  projectile  burst  in  its  bore  may  be  deformed  or  scarred; 
or  it  may  pass  its  accuracy  life  after  having  been  fired  many  rounds. 
A  premature  burst  is  a  very  rare  occurrence,  and,  in  so  far  as  the 
gun  itself  is  involved,  should  not  be  viewed  with  concern.  The 
elastic  strength  of  our  3-inch  field  gun  is  in  excess  of  the  force  of  an 
explosion  of  any  one  of  its  service  projectiles.  The  accuracy  life  of 
a  field  gun  is  a  long  one,  and  perfectly  acceptable  results  should  be 
obtained  with  a  gun  from  which  2,000  rounds  have  been  fired. 

In  the  projectiles  themselves  will  be  found  the  chief  sources  of 
error  not  attributable  to  errors  in  laying  and  fuse  setting.  Different 
projectiles  of  the  same  type  may  not  weigh  the  same.  In  fact,  the 
Ordnance  Department,  for  reasons  of  economy  of  manufacture,  finds 
it  necessary  to  tolerate  a  variation  of  1  per  cent  from  the  prescribed 
weight  of  the  service  3-inch  15-pound  shrapnel. 

The  center  of  gravity  of  a  projectile  may  lie  slightly  off  its  longer 
axis.  This  would  affect  its  accuracy.  Roughness  of  the  projectile 
would  increase  the  resistance  of  the  air  to  its  motion  and  any  error 
in  the  dimensions  of  its  rotating  band  would  affect  its  muzzle  velocity. 

The  muzzle  velocity  is  a  variable  due  to  well-known  causes.  The 
powder  of  different  charges  may  be  of  different  temperatures;  its 
burning  may  not  proceed  identically  each  time;  again,  the  varying 
weights  of  the  projectiles  and  variations  in  the  dimensions  or  defor- 
mation of  the  rotating  band,  all  tend  to  vary  the  actual  muzzle 
velocity  from  that  chosen  as  the  standard.  In  practice  the  errors 
due  to  all  of  tlie  above  causes,  acting  simultaneously,  are  very  small. 
No  serious  error  will  be  committed  in  assuming  the  behavior  of  the 
mean  of  many  shots  to  be  that  of  any  one  of  them. 

The  shrapnel,  set  for  time  burst,  is  subject  to  another  set  of  errors 
due  to  irregularities  in  manufacture  and  the  various  conditions  of  its 


GUNNERY  AND  EXPLOSIVES.  47 

service.  The  handbook  contains  a  description  of  the  service  com- 
bination fuse.  The  time  element  of  this  fuse  regulates  the  point 
of  burst  of  the  shrapnel  for  any  given  trajectory.1  The  time  trains 
are  formed  of  compressed  meal  powder  and  burn  with  a  great  degree 
of  regularity.  Due  to  atmospheric  conditions  during  the  pressing 
of  the  trains  and  due  to  small  variations  in  moisture  content  of  the 
powder  from  day  to  day,  the  time  of  burning  to  any  fuse  setting  is 
found  to  be  slightly  variable.  The  concussion  primer  does  not  act 
precisely  the  same  at  all  times  and  the  powder  pellets,  whose  func- 
tion it  is  to  transmit  the  flame  from  primer  to  upper  train  and  from 
upper  train  to  lower  train,  give  small  variations  which  do  not  seem  to 
yield  entirely  to  refinements  in  the  fuse;  these  irregularities,  together 
with  the  usual  range  errors  (variations  in  the  elements  of  the  trajec- 
tory) are  responsible  for  what  is  known  as  the  dispersion  of  points 
of  burst.  The  dispersion  of  service  fuses  is  carefully  determined  at 
several  ranges  for  each  lot  of  1,000  fuses.  For  the  maximum  range 
of  about  6,500  yards  the  average  dispersion  in  all  lots  of  recent  manu- 
facture is  about  110  yards.  In  other  words,  for  the  same  range  and 
fuse  setting  the  range  difference  between  the  shortest  and  the  longest 
burst  is  110  yards. 

51.  Irregularities  in  the  fuse  due  to  personnel. — For  the 
interest  of  the  student  certain  facts  are  quoted  from  a  report  of  the 
Field  Artillery  Board  upon  the  expenditure  of  2,000  rounds  of  the 
best  available  shrapnel  of  domestic  manufacture.  This  shrapnel 
was  fitted  with  the  F.  A.  21-second  combination  fuse,  model  1907. 
The  quoted  paragraphs  will  indicate  the  necessity  for  a  thoroughly 
trained  personnel. 

"  Throughout  this  firing,  whenever  there  appeared  a  burst  which 
seemed  erratic,  if  the  mechanism  of  fire  then  being  used  and  the 
tactical  conditions  permitted,  an  immediate  examination  was  made 
of  the  laying  and  of  all  sight,  quadrant  and  fuse  setter  readings,  so 
that  the  cause  of  the  irregularity  might  be  determined.  If  the 
mechanism  of  fire  was,  for  example,  'volley  fire '  with  more  than  one 
round,  at  the  conclusion  of  the  problem  the  men  were  ordered  to 
step  back  from  the  guns  and  a  careful  examination  of  the  laying  and 
all  the  different  settings  was  made.  By  this  means  it  was  definitely 
determined  in  every  case  whether  the  responsibility  for  the  irregu- 


48  GUNNERY  AND  EXPLOSIVES. 

larity  of  burst  lay  with  the  fuse  or  the  personnel  of  the  gun  detach- 
ment. The  test  comprised  the  following  problems  and  mechanisms 
of  fire: 

"1.  Six  different  battery  problems  involving  indirect  laying;  tar- 
get, a  hostile  battery,  the  flashes  of  whose  guns  were  visible  over 
crest  concealing  battery;  ammunition  allowance  24  shrapnel,  for  each 
battery. 

"These  problems  required  careful  adjustment  and  were  solved 
in  approximately  15  minutes  each.  There  were  no  erratic  bursts. 

"2.  Six  different  battery  problems  involving  direct  laying;  tar- 
get, an  infantry  skirmish  line;  volley  fire  sweeping  used ; 'ammuni- 
tion allowance,  38  shrapnel  for  each  battery. 

"These  problems  required  rapid  work  on  the  part  of  the  gun  squad 
and  were  solved  in  as  low  as  six  minutes.  There  were  some  erratic 
bursts  in  this  series,  which  investigation  showed  were  due  to  faulty 
laying,  the  gunner  firing  into  an  intermediate  crest  between  the  guns 
and  targets. 

"3.  Six  different  battery  problems  involving  indirect  laying;  tar- 
get, a  battery  concealed  behind  crest,  searched  for  by  successive 
volleys;  ammunition  allowance  for  each  battery,  30  shrapnel. 

"The  requirements  of  these  problems  made  the  solution  necessarily 
slower  than  the  former  problems  and  15  minutes  was  considered  a 
good  exhibition.  No  irregular  bursts. 

"4.  Six  different  battery  problems  involving  zone  fire  with  in- 
direct laying;  target,  a  battery  unlimbering  behind  crest,  with  lim- 
bers and  personnel  represented  as  moving  to  rear  and  flanks;  ammuni- 
tion allowance  for  each  battery,  40  shrapnel. 

"These  problems  were  solved  with  the  gun  squads  working  with 
the  greatest  rapidity  possible,  a  time  of  as  low  as  four  minutes  being 
obtained.  No  irregular  bursts. 

"5.  Six  different  battery  problems,  involving  zone  fire  sweeping, 
with  direct  laying;  target,  a  large  body  of  infantry,  covering  a  space 
of  some  200  by  300  yards;  ammunition  allowance  for  each  battery, 
56  shrapnel. 

' '  These  problems  required  great  speed  and  were  solved  in  as  short 
a  time  as  three  and  one-half  minutes. 

"In  this  series  were  noticed  quite  a  number  of  irregular  bursts. 
In  one  battery,  very  short  bursts  were  found  to  be  due  to  the  chief  of 
platoon  giving  the  range  1,000  yards  less  than  the  one  announced  by 
the  captain. 

"In  another  battery,  very  high  bursts  were  found  to  be  due  to 
defective  laying  on  the  part  of  the  gunner. 


GUNNERY  AND  EXPLOSIVES.  49 

"6.  Six  different  battery  problems,  involving  direct  laying  at  a 
moving  target  representing  cavalry  emerging  from  concealment  some 
1,200  yards  away  from  the  position  of  the  battery  and  charging  the 
guns.  The  sleds  in  each  case  continued  the  run  until  they  reached 
the  guns;  ammunition  allowance  for  each  battery,  28  shrapnel. 

"This  problem  involved  the  most  rapid  work  possible  at  the  fuse 
setters,  and  was  solved  in  as  low  as  1  minute  and  30  seconds  from  the 
first  to  last  shot  of  the  series.  As  the  targets  were  moving  with  great 
rapidity,  it  was  practically  impossible  to  determine  irregularities 
in  range  with  reference  to  the  targets,  if  any  existed.  The  action 
of  the  fuse  appeared  normal. 

"  7.  Two  battalion  problems  involving  indirect  laying;  target,  a 
line  of  hostile  infantry,  approximately  equal  to  that  of  the  bat- 
talion; ammunition  allowance,  42  shrapnel  for  each  battalion. 

"This  firing  was  relatively  quick  for  the  size  of  the  unit  and  the 
method  of  laying,  consuming  some  10  minutes,  and  no  erratic  bursts 
were  noted. 

"8.  Two  battalion  problems,  involving  indirect  laying,  with  the 
target  representing  a  hostile  battalion,  %  whose  position  behind  a 
crest  is  revealed  by  the  flashes  of  its  guns;  ammunition  allowance, 
42  shrapnel  for  each  battalion. 

"This  firing  was  relatively  quick,  also,  consuming  some  10  min- 
utes in  the  lowest  case,  and  no  irregular  bursts  were  noted. 

"9.  Two  battalion  problems,  involving  indirect  laying,  against  a 
hostile  battery,  the  three  batteries  of  the  battalion  being  separated; 
ammunition  allowance,  62  rounds  of  shrapnel  for  each  battalion. 

"These  problems  were  relatively  slow,  the  quickest  consuming 
some  20  minutes.  Some  irregularity  of  burst  was  noticed.  One 
shot,  which  burst  a  considerable  distance  beyond  the  target,  was 
judged  a  ricochet,  while  in  case  of  one  which  burst  short  and  high 
it  was  impossible  to  determine  any  external  error.  This  erratic 
burst  was  ascribed  to  some  defect  in  the  fuse. 

"10.  One  regimental  problem,  involving  indirect  laying,  target 
a  line  of  infantry  about  equal  in  length  to  that  of  the  regiment; 
ammunition  allowance,  68  shrapnel. 

"The  firing  was  deliberate,  and  no  erratic  bursts  were  noted. 

"11.  One  regimental  problem,  with  the  battalions  separated, 
involving  indirect  laying,  against  a  hostile  battalion  of  field  artil- 
lery; ammunition  allowance,  84  shrapnel. 

"The  firing  was  deliberate.  Eight  quite  high  bursts  were  noted 
in  the  final  regimental  volley,  which  were  ascribed  to  the  respec- 

96609°— 11 i 


50  GUNNERY  AND  EXPLOSIVES. 

tive  No.  Is  of  pieces  which  had  not  been  used  in  tjie  adjustment 
and  who  did  not  carefully  center  their  bubbles  in  the  final  volley. 

"12.1  One  regimental  problem,  indirect  laying;  ammunition 
allowance  140  shrapnel.  The  target  in  this  case  was  a  line  of  kneel- 
ing figures  along  the  military  crest  of  a  ridge,  with  gentle  slope, 
near  the  target  of  perhaps  one  on  twenty.  At  distances  of  100,  200j 
and  300  yards  from  the  target  were  placed  standing  figures,  repre- 
senting lines  of  advancing  infantry.  The  fire  was  adjusted  on  the 
target  and  all  figures  marked,  so  as  to  eliminate  hits  due  to  adjust- 
ment. Fire  was  then  resumed,  and  subsequent  inspection  of  the 
target  showed  no  hits  on  either  the  200  or  300  yard  lines  and  only 
three  hits  on  the  100-yard  line.  The  target'  was  riddled.  This 
was  a  very  important  test,  and  shows  that  *  *  *  our  infantry 
can  advance  to  within  remarkably  short  distances  of  the  enemy 
without  danger  from  the  supporting  artillery. 

"13.  Two  battalion  problems;  horse  artillery  firing  upon  defeated 
infantry;  direct  laying;  ammunition  allowance,  42  shrapnel  for 
each  battalion. 

"These  problems  were  solved  very  rapidly — inside  of  three  min- 
utes each — and  no  erratic  bursts  were  noted." 

It  will  be  seen  that  among  the  irregular  bursts  noted  all  but  one 
were  due  to  the  personnel. 

52.  Accuracy  and  probability  of  fire. — As  a  result  of  inaccu- 
racies, due  to  faulty  materiel  and  to  errors  committed  by  the  per- 
sonnel, two  successive  rounds  rarely,  if  ever,  fall  in  exactly  the  same 
place.  .  In  practice  this  means  that  the  trajectories  of  a  number  of 
projectiles  fired  under  as  nearly  as  possible  the  same 'conditions  do 
not  coincide,  but  form  a  cone  about  the  mean  trajectory  as  an  axis. 
This  cone  is  called  the  sheaf  of  fire,  the  ground  section  of  which  is 
an  ellipse,  with  the  longer  axis  in  the  direction  of  the  range.  In 
determining  the  accuracy  of  a  gun  at  any  given  range  and  under 
any  special  conditions  a  number  of  shots  are  fired  under  the  given 
conditions.  The  firing  is  done  in  such  manner  as  to  make  the  cir- 
cumstances governing  all  rounds  as  nearly  alike  as  possible,  and 
the  point  of  fall  of  each  shot  is  plotted,  usually  with  reference  to 
the  assumed  origin.  The  coordinates  x  and  y  of  each  shot  mark  are 
measured  with  respect  to  two  rectangular  axes  X  and  Y,  intersect- 
ing at  the  assumed  origin.  The  sum  of  the  abscissas  divided  by 
the  number  of  the  shots  is  the  mean  abscissa,  and  the  sum  of  the 

i  The  results  of  this  firing  are  given  in  Chapter  IV. 


GUNNERY  AND  EXPLOSIVES. 


51 


ordinates  divided  by  this  number  is  the  mean  ordinate.  The  mean 
abscissa  xm  and  the  mean  ordinate  ym  are  the  coordinates  of  the 
center  of  impact.  The  actual  distance  of  each  shot  from  the  center 
of  impact  is  the  absolute  deviation  for  the  shot,  and  the  mean  of  the 
absolute  deviations  is  the  mean  absolute  deviation  for  the  group. 
By  comparing  the  mean  absolute  deviations  of  different  groups  of 
shots  we  may  arrive  at  the  comparative  accuracy  of  different  guns 
or  of  the  same  gun  under  different  conditions  of  firing. 

Example:  In  a  test  by  the  Field  Artillery  Board  the  3-inch  field 
gun  was  fired  for  accuracy.  The  target  was  horizontal  and  1,900 
yards  from  the  gun.  The  coordinates  of  each  shot  were  measured 
from  a  line  Y  normal  to  the  plane  of  fire,  1,900  yards  from  gun, 
and  a  line  X,  parallel  to  the  plane  of  fire  and  5  yards  to  the  left  of  it. 


Number  of  shot. 

Coordinates. 

Deviations. 

Range. 

Direction. 

Range. 

Direction. 

1 

Yards. 
39 
35 

22 
69 
44 
58 
34 
84 
32 
42 
25 
50 
40 
62 
50 
24 
28 
70 
57 
45 
55 
67 
60 
60 

Yards. 
10.0 
17.0 
6.5 
3.25 
9.5 
5.5 
5.5 
3.5 
6.0 
7.5 
1.5 
2.5 
3.0 
7.5 
5.0 
6.0 
5.0 
3.75 
5.0 
.5 

Yards. 
9 
13 
26 
21 
4 
10 
14 
36 
16 
6 
23 
2 
8 
14 
2 
24 
20 
22 
9 
3 
7 
19 
12 
12 

Yards. 
4.3 
11.3 

.8 
2.45 
3.8 
2 

'.2 
2.2 
.3 

1.8 
4.2 
3.2 
2.7 
1.8 
.7 
.3 
.7 
1.95 
.7 
5.2 

2       

3 

4  

5 

6  

7 

8  

Q 

10 

11.. 

12 

13  

14.    . 

15 

16  

17 

18  

19 

20 

21.. 

22 

23  

24. 

24)1,152 

20)114 

24)332 

20)48.8 

48 

5.7 

13.8 

2.44 

52  GUNNERY  AND  EXPLOSIVES. 

The  coordinates  of  the  center  of  impact  are:  In  the  direction  of 
the  range,  48  yards;  normal  to  range,  5.7  yards.  The  mean  devia- 
tions from  the  center  of  impact  are:  In  direction  of  range,  13.8 
yards;  normal  to  range,  2.44  yards.  The  mean  absolute  deviation = 


v 


2  2  

+ =y  196. 39=14  yards,  approximately. 

lo.o       Z.44 


53.  Total  rectangle. — For  convenience,  it  is  usual  to  express 
the  elliptical  area  or  ground  section  of  the  sheaf  of  fire  in  terms  of 
the  enveloping  rectangle.     An  examination  of  the  table  above  will 
show  that  all  the  shots  were  contained  in  a  rectangle  62  yards  long 
by  16.5  yards  wide.     This  rectangle  is  known  as  the  100  per  cent  or 
total  rectangle. 

54.  Probability  of  fire. — The  principal  value  of  the  preceding 
examination  into  the  behavior  of  the  3-inch  gun  is  to  obtain  some 
idea  of  the  number  of  hits  that  may  be  expected  when  the  personnel 
is  performing  perfectly.     The  test  from  which  the  above  record  is 
taken  was  supervised  carefully  and  was  supposedly  free  from  per- 
sonal errors.     It  has  been  seen  that  the  mean  range  deviation  is  13.8 
yards  and  that  the  mean  direction  deviation  is  2.44  yards.     These 
mean  deviations  or  mean  errors  are  slightly  in  excess  of  the  probable 
errors,  due  to  the  fact  that  large  errors  are  less  frequent  than  small 
errors.     In  other  words,  the  great  majority  of  shots  in  a  group  are 
relatively  near  the  center  of  impact.     The  probable  error  is  ob- 
tained from  the  mean  error  by  multiplying  the  latter  by  0.846.     For 
the  case  under  consideration  the  probable  error  in  range  equals 
13. 8X. 846=11. 67     yards;    the     probable     error     in     direction     is 
2.44X. 846=2.06  yards. 

55.  The  50  per  cent  rectangle. — In  a  group  of  shots  one-half 
will  fall  over  or  short  of  the  center  of  impact  by  amounts  equal  to  or 
less  than  the  probable  error.     As  half  of  these  will  be  short  and  half 
over,  we  may  construct  the  50  per  cent  rectangle  as  follows:  At 
distances  equal  to  the  probable  range  error,  draw  on  each  side  of 
the  center  of  impact  a  line  normal  to  the  line  joining  gun  and  cen- 
ter of  impact;  at  distances  equal  to  the  probable  direction  error, 
draw  on  each  side  of  the  center  of  impact  a  line  parallel  to  the  line 
joining  gun  and  center  of  impact;  the  four  lines  thus  constructed 
will  form  the  50  per  cent  rectangle. 

Knowing  the  range  and  direction  errors  and  the  angle  of  fall  at 
any  range,  the  50  per  cent  rectangle  may  be  constructed  for  hits  on 
a  vertical  target. 


GUNNERY  AND  EXPLOSIVES. 


53 


56.  Probable  error  of  3-inch  field  gun. — The  following  table, 
based  upon  a  test  by  the  Field  Artillery  Board,  contains  the  prob- 
able range  and  direction  errors  for  the  weapon  under  consideration: 


Probable 

Probable 

Range. 

error  in 

error  m 

range. 

direction. 

Yards. 

Yards. 

Yards. 

2,000  

12 

2 

2,500  

15 

2.5 

3,000  

15 

3.0 

3,500  

16 

3.5 

4,000  

17 

4.0 

57.  Application  of  probabilities. — The  dimensions  of  the  50 
per  cent  rectangle  are  taken  as  the  unit  of  comparison  and,  based 
upon  the  theory  of  errors,  the  following  table  gives  the  dimensions 
of  rectangles  of  other  percentages  in  terms  of  the  unit  dimensions: 


Per 
cent. 

Factor 
Z/ZL 

Per 
cent. 

Factor 
Z/Zi. 

Per 

cent. 

Factor 
Z/Zj. 

Per 
cent. 

Factor 

Z/Zi. 

Per 
cent. 

Factor 
Z/ZL 

1 

0.02 

21 

0.40 

41 

0.80 

61 

1.27 

81 

1.94 

2 

.04 

22 

.41 

42 

.82 

62 

1.30 

82 

1.98 

3 

.06 

23 

.43 

43 

.84 

63 

1.33 

83 

2.03 

4 

.07 

24 

.45 

44 

.86 

64 

1.36 

84 

2.08 

5 

.09 

25 

.47  ' 

45 

.89 

65 

1.39 

85 

2.13 

6 

.11 

26 

.49 

46 

.91 

66 

1.42 

86 

2.18 

7 

.18 

27 

.51 

47 

.93 

67 

1.45 

87 

2.24 

8 

.15 

28 

.53 

48 

.95 

68 

1.48 

88 

2.30 

9 

.17 

29 

.55 

49 

.98 

69 

1.51 

89 

2.37 

10 

.18 

30 

.57 

50 

1.00 

70 

1.54 

90 

2.44 

11 

.20 

31 

.59 

51 

1.02 

71 

1.57 

91 

2.52 

12 

.22 

32 

.61 

52 

1.04 

72 

1.60 

92 

2.60 

13 

.24 

33 

.63 

53 

1.07 

73 

1.64 

93 

2.69 

14 

.26 

34 

.65  ' 

54 

1.09 

74 

1.67 

94 

2.78 

15 

.28 

35 

.67 

55 

1.12 

75 

1.71 

95 

2.91 

16 

.30 

36 

.70 

56 

1.14 

76 

1.74 

96 

3.04 

17 

.32 

37 

.72 

•  57 

1.17 

77 

1.78 

97 

3.22 

18 

.34 

38 

.74 

58 

1.19 

78 

1.82 

98 

3.45 

19 

.36 

39 

.76 

59 

1.22 

79 

1.86 

99 

3.82 

20 

.38 

40 

.78 

60 

1.25 

80 

1.90 

100 

54  GUNNERY  AND  EXPLOSIVES. 

The  factor  Z/Zj  above  shows  the  dimensions,  in  terms  of  those  of 
the  50  per  cent  rectangle,  of  the  rectangle  whose  percentage  is  given 
in  the  column  next  on  its  left. 

For  instance,  if  the  50  per  cent  rectangle  is  24  yards  long  and  4 
yards  wide  the  60  per  cent  rectangle  will  be  24X1.25=30  yards  long 
and  4X1.25=5  yards  wide;  the  82  J  per  cent  rectangle  will  be  48 
yards  long  and  8  yards  wide.  The  99 J  per  cent  rectangle  is  four 
times  as  long  and  four  times  as  wide.  Practically  this  rectangle  is 
the  enveloping  rectangle. 

The  use  of  the  above  table  is  illustrated  by  the  following: 

Example:  In  firing  with  shell,  what  is  the  chance  of  hitting  a 
vertical  surface  6  feet  high  and  12  feet  wide  at  a  range  of  3,500  yards? 

From  the  table  in  paragraph  56  it  is  seen  that  50  per  cent  of  the 
rounds  should  fall  in  a  rectangle  32  yards  long  and  7  yards  wide. 
The  angle  of  fall  is  1  on  5.8;  hence  the  vertical  50  per  cent  rectangle 
will  be  5.5  yards  high  by  7  yards  wide. 

The  width  of  the  target  is  4  yards  or  0.57  of  7  yards.  In  the  table 
the  factor  opposite  0.57  is  30  per  cent,  hence  30  per  cent  of  the  shots 
will  be  correct  for  line. 

The  height  of  the  target  is  2  yards  or  0.36  of  5.5.  In  the  table  the 
factor  opposite  0.36  is  19  per  cent;  hence  19  per  cent  of  the  shots  will 
be  correct  for  elevation. 

The  probability  that  one  shot  will  hit  the  target  is  0.19X0.30=5.7 
per  cent;  100  rounds  should  give  5.7  hits  or  approximately  17  rounds 
per  hit. 


CHAPTER  VIII. 

THE    SINGLE    SHRAPNEL. 

58.  The  purpose. — The  attack  of  personnel  would  be  a  very 
difficult  matter  without  shrapnel.     The  high  explosive  effect  cf 
percussion  shell  is  restricted  to  a  very  small  area,  whereas  the  shrap- 
nel, burst  properly  in  air,  distributes  a  large  number  of  projectiles, 
each  one  of  which  is  capable  of  killing  a  man  or  horse  at  reasonable 
distances  from  point  of  burst. 

59.  The   bursting   of  shrapnel. — The   shrapnel   case   is   the 
vehicle  for  transfer  of  the  shrapnel  balls  from  gun  to  bursting  point. 
At  this  point  the  powder  charge  in  its  base  is  ignited  and  the  balls 
are  driven  out  with  increased  velocity.     After  the  time  burst  each 
shrapnel  ball  pursues  its  own  trajectory  depending  upon  its  velocity 
and  initial  direction.     The  projectile  has  a  motion  of  rotation  due  to 
which  the  balls  are  thrown  away  from  the  trajectory  which  the 
shrapnel  would  have  followed  had  it  not  burst  in  air.     The  paths 
of  all  the  shrapnel  balls  taken  collectively  form  a  cone  called  the 
cone  of  dispersion.     The  ground  section  of  this  cone  is  an  irregular 
oval  with  its  longer  axis  approximately  in  the  plane  of  fire.     The 
dimensions  of  this  section  will  vary  with  the  angle  of  fall,  the  height 
of  burst,  the  slope  of  the  ground,  and  the  relation  between  the 
linear  and  rotational  velocities  at  instant  of  time  burst. 

60.  Angle  of  opening. — The  angle  at  the  apex  of  the  cone  of 
dispersion  may  be  computed  in  the  following  manner:  At  the  instant 
of  time  burst  the  projectile  has  a  remaining  velocity  in  the  direction 
of  the  range  and  a  rotational  velocity  about  its  own  longitudinal  axis. 
The  balls  are  given  an  additional  velocity  by  the  base  bursting 
charge.     Each  ball  upon  emerging  from  the  shrapnel  case  has  a  veloc- 
ity in  the  direction  of  the  range  equal  to  the  sum  of  the  remaining 
velocity  of  the  projectile  and  that  velocity  imparted  to  it  by  the 
bursting  charge;  in  a  direction  normal  to  and  away  from  the  tra- 
jectory it  has  velocity  due  to  the  projectile's  rotation. 

55 


56 


GUNNERY  AND  EXPLOSIVES. 


In  figure  9  assume  A  as  the  origin  of  the  cone  of  dispersion  (point 
of  burst).  Suppose  AE— 800  foot-seconds  to  represent  the  remaining 
velocity  of  the  projectile  at  point  of  burst,  and  ED=200  foot-seconds 
to  represent  the  increase  in  velocity  due  to  bursting  charge.  Neglect- 
ing the  resistance  of  the  air  and  attraction  due  to  gravity  the  balls 
would  proceed  along  the  line  ADX,  if,  at  the  time  of  burst,  the  pro- 
jectile had  no  motion  of  rotation. 

As  the  projectile  is  rotating,  let  BD=100  foot-seconds,  represent 
its  velocity  in  a  direction  normal  to  the  trajectory  ADX.  It  will  be 
seen,  therefore,  that  at  the  end  of  1  second  the  highest  ball  in  the 
cone  of  balls  will  be  found  at  B,  having  proceeded  1,000  feet  in  the 
direction  AD'  and  100  feet  upward.  Such  being  the  case  we  may 
write 

Tangent  BAD=BD/AD 

BAD  is  one-half  the  angle  of  opening. 


Determination  of  BD.  —  Figure  10  is  a  normal  cross  section  of  a 
projectile  making  n  clockwise  revolutions  per  second.  If  a  particle 
at  B  be  released,  it  would  leave  the  circumference  along  the  tangent 

BD  with  a  linear  velocity  of  nX-  feet  per  second,  hence  — 


BD=-«-  foot-seconds. 

D 


Example:  The  muzzle  velocity  of  the  service  3-inch  shrapnel  is 
1,700  foot-seconds;  the  bursting  charge  adds  200  foot-seconds;  at  the 
muzzle  of  the  gun  the  projectile  makes  one  turn  in  25  calibers;  as- 
sume r7  (fig.  10)  equal  to  1  inch. 


GUNNERY  AND  EXPLOSIVES. 


57 


Solution : 

AD  =  1, 700+200=1, 900  foot-seconds  (fig.  9).     The  projectile  makes 
one  turn  in  25  calibers,  or  6.25  feet. 

1,700-^-6.25=272  revolutions  per  second. 


BD= 


272X;rXl 
IT 


=142  foot-seconds. 


Tangent  BAD- 


BAD  =4°  16X,  which  is  one-half  the  angle  of  opening  when  the 
burst  is  at  the  muzzle  of 
the  gun. 

At  1,000  yards  the  re- 
maining  velocity  =1,270 
foot  -seconds.  Assume 
that  the  rotational  veloc- 
ity of  the  projectile  has 
fallen  off  8  per  cent, 
which  is  the  usual  as- 
sumption for  1,000  yards, 


then 
onds. 


BD=131  foot-sec- 


BAD=tan-1 


131 
M70 


=5 


The  whole  angle  of 
opening,  BAG,  figure  9, 
is  therefore  10°  1C'. 

Actually  the  angle  of 
opening  is  greater  than 
the  computed  angle. 
The  first  layer  of  balls 
emerging  from  the  shrap- 
nel case  does  not  get  the  full  benefit  of  the  driving  effect  of  the 
bursting  charge;  balls  no  doubt  impact  against  each  other,  particu- 
larly as  those  with  the  greatest  velocity  emerge  last;   finally,  the 
expanding  gases  of  the  driving  charge  assist  in  opening  out  the  cone 


58 


GUNNERY  AND  EXPLOSIVES. 


of   dispersion.     Tests  made  at   the  Sandy  Hook   Proving  Ground 
show  that  at  1,000  yards  the  angle  of  opening  is  very  nearly  13°. 

As  a  result  of  actual  firings  it  has  been  found  that  the  angle  of 
opening  increases  as  the  range  increases.  The  table  below  is  based 
upon  experiment: 


Range. 

Angle  of 
opening. 

Log.  tan. 

Yards. 

0             , 

2,000 

14    13 

9.  40385 

2,500 

15    00 

.  42845 

3,000 

15    42 

.  44896 

3,500 

16    18 

.46591 

4,000 

16    52 

.  48134 

4,500 

17    26 

.  49654 

61.  Height  of  burst  for  desired  effect. — The  theory  upon 
which  the  proper  height  of  burst  of  a  well-adjusted  shrapnel  has  been 
based  is  that  for  every  square  yard  of  a  vertical  target  there  should 
be  one  ball.  It  will  be  seen,  therefore,  that  if  the  cone  of  dispersion 
be  intersected  by  a  plane  normal  to  its  axis,  at  such  distance  from 
the  point  of  burst  that  the  area  of  the  section  in  square  yards  will 
equal  the  number  of  balls  in  the  shrapnel,  this  distance  in  yards 
multiplied  by  the  sine  of  the  angle  of  fall  will  give  the  proper  height 
of  burst  in  yards.  Thus,  in  figure  11: 

Let  A  be  point  in  trajectory  OA  at  which  the  shrapnel  bursts. 

0=one-half  angle  of  opening. 
AD=distance  to  normal  section  BC. 
r=radius  of  BmCn. 
co Bangle  of  fall. 

N=number  of  balls  in  shrapnel =250. 
Then  r=AD  tan  0 
and  area  of  normal  section=7r  r2. 

r=8.92  yards. 

As  would  be  expected,  the  radius  of  the  normal  section  containing 
1  ball  per  square  yard  is  constant.  The  distance 

8.92 


AD= 


"tan  6    tan  0 


GUNNERY  AND  EXPLOSIVES. 


59 


The  table  below  sets  forth  information  concerning  the  burst 
interval  for  the  3-inch  field  gun  at  various  ranges.  8  is  one-half  the 
angle  of  opening  corresponding  to  the  assumed  range. 


Range. 

6. 

1  hit  per  square  yard. 

Height  of  burst—  3  mils. 

Interval 
AD. 

Front  cov- 
ered. 

Horizontal 
interval. 

Front  cov- 
ered. 

Yards. 
1.000 
2,000 
2,500 
3,000 
3,500 
4,000 
4,500 

6    30 
7      6 
7    30 
7    51 
8    09 
8    26 
8    43 

Yards. 
78.3 
72.2 
68.4 
65.3 
62.3 
60.2 
58.2 

Yards. 
17.84 
17  84 
17  84 
17.84 
17.84 
17*84 
17.84 

Yards. 
118.2 
85.4 
73.5 
66.6 
60.9 
56.4 
51.3 

Yards. 
26.9 
20.6 
19.2 
18.2, 
17.4 
16.7 
15.7 

An  examination  of  the  above  table  will  show  that  between  2,500 
and  4,000  yards  the  height  of  burst  of  3  mils  gives  approximately  the 
desired  density  of  fire.  At  ranges  less  than  2,500  yards  the  front 
covered  by  a  burst  3  mils  high  is  greatly  increased  hence  the  density 
of  fire  is  diminished. 


(Hg.ll), 


62.  Effective  range  of  shrapnel  balls. — It  has  been  seen  that 
when  a  shrapnel  bursts  in  air  the  balls  are  driven  out  with  an 
increased  velocity  of  approximately  200  feet  per  second.  The  high- 
est shrapnel  ball  in  the  cone  of  dispersion  moves  along  a  line  inclined 


60 


GUNNERY  AND  EXPLOSIVES. 


upward  to  the  trajectory  of  the  shrapnel  continued,  and  will  have 
the  greatest  range  of  any  ball.  The  actual  range  of  shrapnel  balls  is 
ordinarily  greater  than  the  effective  range.  The  effective  range  is 
the  distance  from  point  of  burst  to  a  point  in  the  trajectory  of  the 
shrapnel  ball  where  its  remaining  energy  is  just  sufficient  to  disable 
a  man.  In  this  country  it  has  been  assumed  that  an  energy  of  58 
foot-pounds  will  serve  the  purpose,  hence  the  effective  range  would 
be  measured  from  the  point  of  burst  to  the  point  where  the  ball  has 
a  remaining  velocity  of  v  feet  per  second,  such  that 


V=\ 


=~ 


9  *s  the  acceleration  due  to  gravity  and  W 

is  the  weight  of  a  shrapnel  ball,  in  pounds. 

The  shrapnel  described  in  the  handbook  is  filled  with  balls  weigh- 
ing each  167  grains,  or  1/42  pound.     W  therefore  equals  1/42,  and 

•v=Vll6X32.2X42=396  foot-seconds. 
An  examination  of  the  following  table  will  be  of  interest: 
Calculated  values  of  the  effective  ranges  of  shrapnel  balls. 


Number  of 
balls  per 
pound. 

Remaining  veloci- 
ty    correspond- 
ing    to     energy 
of— 

Effective  range  of  balls  be- 
yond   points   of   burst   at 
ranges  of  approximately— 

58  foot- 
pounds. 

116  foot- 
pounds. 

1,500 
yards. 

2,500 
yards. 

4,500 
yards. 

37.74 
37.74 

i  41.15 
141.15 

45.45 
45.45 

Ft.  sees. 
374 

Ft.  sees. 

Yards. 
425 
252 

386 
230 

357 
208 

Yards. 
405 
232 

366 
211 

"     337 
189 

Yards. 
371 

198 

336 
177 

304 
156 

532 

394 

554 

410 

581 

i  Corresponds  very  nearly  with  service  balls 


GUNNERY  AND  EXPLOSIVES.  61 

In  practice  the  effective  ranges  are  found  to  be  somewhat  less  than 
those  calculated,  particularly  at  long  ranges,  where  the  angle  of  fall 


SERVICE   TESTS. 

The  Field  Artillery  Board  during  the  fall  of  1906  conducted  cer- 
tain firings,  the  principal  object  of  which  was  to  determine  the  effect 
produced  by  a  single  well-adjusted  shrapnel  and  groups  of  such 
projectiles.  Firings  were  conducted  at  ranges  of  1,900,  2,800,  3,500, 
3,700,  and  4,259  yards  against  eight  board  targets,  each  40  yards  wide 
and  2  yards  high,  made  of  1-inch  lumber.  These  targets  were  located 
50  yards  apart  in  the  direction  of  the  range.  Fire  was  first  adjusted 
on  an  auxiliary  target  100  yards  to  the  flank  of  the  third  target,  and 
then  shifted  to  the  board  target.  All  incidents  of  fire  were  carefully 
supervised.  Service  ammunition  was  used.  In  drawing  conclu- 
sions concerning  the  effect  produced  only  the  bullets  which  per- 
forated the  target  or  which  embedded  themselves  in  it  were  regarded 
as  effective.  Bullets  which  merely  dented  the  target  were  regarded 
as  ineffective,  though  the  board  was  of  the  opinion  that  many  of  these 
would  have  put  a  man  out  of  action. 

The  board  concluded  as  to  the  effect  produced  by  a  single  well- 
adjusted  shrapnel: 

(a)  The  front  (or  width)  of  target  effectively  covered  at  the  point 
of  fall  is  between  18  and  25  yards,  being  nearer  18  at  the  long  ranges 
and  nearer  25  at  the  short  and  midranges. 

(b)  At  ranges  up  to  3,000  yards,  the  depth  effectively  searched  is 
about  200  yards,  i.  e.,  about  50  yards  in  front  of  the  target  and  about 
150  yards  in  rear  of  it. 

(c)  At  longer  ranges  (from  3,500  to  4,500  yards)  the  depth  effec- 
tively searched  is  about  125  yards,  i.  e.,  about  25  yards  in  front  of 
the  target  and  about  100  yards  in  rear  of  it. 

The  above  conclusions  are  well  within  limits; -actually,  at  a  range 
of  1,900  yards,  there  were  occasional  effective  hits  on  seven  targets, 
hence  the  bullets  must  have  had  an  effective  range  of  at  least  300 
yards.  At  2,800  yards  range  there  were  effective  hits  on  six  targets  or 
over  250  yards;  at  3,500  the  effective  hits  were  spread  over  at  least 
200  yards  and  at  4,259  yards  at  least  150  yards.  If  the  interval  of 
burst  in  front  of  the  first  target  struck  be  considered  and,  furthermore, 
if  it  be  considered  that  the  last  target  struck  was  not  necessarily  at 
the  limit  of  effect,  the  actual  values  of  the  effective  ranges  accord 
closely  with  the  calculated  values  tabulated  above. 


62  GUNNERY  AND  EXPLOSIVES. 

63.  Density  of  fire. — The  density  of  fire  in  the  case  of  a  well- 
adjusted  shrapnel  is  one  ball  per  square  yard.     In  order  to  attain  this 
density  the  shrapnel  must  burst  at  an  interval  AD  (fig.  11)  in  front  of 
the  target  such  that 

AT,      8-92 
AD~tan  6 

As  AD  increases,  the  area  of  the  section  BC  of  the  cone  of  dispersion 
increases  and  the  density  (balls  per  square  yard)  decreases. 

r=AD  tan  S 
xri=K=n  (AD  tan  0)2 

Density  in  balls  per  square  yard= 

250 
n  (AD  tan  0)2 

or  the  density  varies  inversely  as  the  square  of  the  interval  of  burst. 
It  follows  from  the  above  that  the  number  of  hits  on  any  target  due 
to  any  shrapnel  burst  may  be  computed. 
The  following  should  be  known: 
Exposed  area  of  target. 
Number  of  balls  in  shrapnel. 
Interval  of  burst. 
Angle  of  opening. 
Angle  of  fall. 

It  has  been  assumed  that  the  trajectory  of  the  projectile  continued 
passes  through  the  target. 

Example:  What  is  the  density  of  hits  of  the  service  shrapnel  at  a 

range  of  2,750  yards  with  interval  of  burst  of  42  yards?  of  104  yards? 

Example:  How  many  hits  may  be  expected  from  one  round  of  the 

service  shrapnel,  the  range  being  3,400  yards,  the  interval  of  burst 

92  yards,  on  a  target  7  yards  wide  and  6  feet  high? 

Example:  How  many  hits  should  be  made  at  2,300  yards,  when 
firing  at  a  line  of  skirmishers  lying  down  (each  man  occupying  a 
front  of  0.85  yard),  with  intervals  of  burst  of  50,  100,  150,  and  200 
yards? 

64.  The  ground  section. — The  ground  section  of  the  cone  of 
dispersion  may  be  computed,  but  it  is  simpler  to  construct  it  to 
scale.     The  point  of  burst  should  be  located  on  cross-section  paper; 


GUNNERY  AND  EXPLOSIVES.  63 

then,  from  the  proper  relations,  the  angle  of  opening  is  determined  and 
laid  off  in  such  manner  that  it  will  be  bisected  by  the  trajectory  con- 
tinued. The  ground  section  is  known  as  the  zone  of  dispersion. 

By  locating  the  points  in  which  the  limiting  bullets  of  the  cone  of 
dispersion  pierce  the  horizontal  plane  the  horizontal  zone  of  disper- 
sion may  be  constructed.  Such  drawing  would  show  the  influence 
of  the  ground  upon  the  depth  of  effect  of  a  shrapnel.  If,  for  example, 
it  be  supposed  that  the  ground  at  the  target  has  an  upward  slope  of 
5°,  it  is  necessary  only  to  construct  the  points  in  which  the  outer 
bullets  pierce  the  inclined  plane.  These  points  limit  the  new  zone 
of  dispersion.  It  may  also  be  seen  from  such  drawing  how  the  width 
of  the  zone  of  dispersion  falls  off  with  small  heights  of  burst.  For 
height  of  burst  greater  than  the  normal  the  zone  of  dispersion  will  be 
wider.  In  the  latter  case  the  danger  of  going  over  the  target  at  short 
intervals  of  burst  will  be  greater  also. 

The  curve  of  the  descending  branch  of  the  trajectory  diminishes 
the  effect,  and  especially  the  depth  of  effect,  of  shrapnel.  The 
flatter  the  trajectory  the  greater  the  depth  of  effect. 

A  study  of  the  ground  section  of  cones  of  dispersion  should  be  made 
in  connection  with  the  effective  ranges  of  shrapnel  balls.  It  will  be 
found  that  many  balls  impacting  near  the  outer  limit  of  a  ground 
section  are  ineffective  due  to  lack  of  man-killing  energy. 


CHAPTER  IX. 

THE    EFFECT    OF   A    GROUP    OF    SHRAPNEL. 

60.  General  considerations. — In  the  preceding  chapter  the 
behavior  of  a  single  shrapnel,  at  and  subsequent  to  its  burst,  has 
been  analyzed.  With  the  knowledge  gained  during  the  study  of 
the  chapter  referred  to,  the  conception  of  shrapnel  fire  may  be 
readily  extended  to  include  the  group.  It  has  been  seen  that  the 
effect  of  a  single  shrapnel  depends  upon  and  varies  with — 

(a)  The  number  of  balls,  N. 

(6)  The  angle  of  opening,  2  6. 

(c)  The  interval  of  burst. 

(d)  The  height  of  burst.  ' 
e)  The  energy  of  the  balls. 


(/)  -The  angle  of  fall, 

e,  kno 


hence,  knowing  these  quantities  for  any  particular  case,  the  number 
of  hits  (effective  or  noneffective)  on  a  given  target,  may  be  com- 
puted. Similarly,  though  with  obvious  modifications,  the  effect 
of  a  group  of  shrapnel  may  be  determined. 

66.  Hits  from  a  group  of  shrapnel. — Let  it  be  supposed  that 
each  shrapnel  of  the  group  bursts  at  the  same  point  in  front  of  the 
assumed  target.  If  Q  men  are  within  the  effective  zone  of  disper- 
sion, a  certain  number  m,  depending  upon  the  interval  of  burst,  will 
be  killed  by  the  first  shot  of  the  group.  The  number,  m,  may  be 
expressed  as  some  fraction  of  Q  or  m=Qx.  The  men  killed  by  any 
shot  will  be  a  fixed  fraction  (x)  of  those  left  standing  after  the  next 
preceding  shot,  but  the  number  of  killed  per  round  grows  less  for 
each  succeeding  round. 

Thus,  in  the  first  round,  Qx  are  killed  and  Q  —  Qz=Q(l  —x)  survive. 

In  the  second  round,  Q(l—  x)x  are  killed  and  Q(l—  x)2  survive; 
in  the  two  rounds  Qx-Q,(I-x)x  or  Q(l-(l-z)2)  will  be  killed. 

We  may  write,  therefore, 

In  the  nth  round  Q(l—  x)  n— lx  are  killed. 

64 


GUNNERY  AND  EXPLOSIVES.  65 

After  the  nth  round  Q(  1—  a;)  n  survive  and  during  n  rounds  Q(l  — 
(1—  x)n)  have  been  killed. 
It  is  obvious  that 


67.  Determination  of  x.  —  As  stated  before,  the  number  of  men 
in  any  surviving  group  wholly  and  effectively  covered  by  the  cone 
of  dispersion  will  be  diminished  by  a  definite  percentage  x  at  each 
successive  round.  It  is  possible  that  there  may  be  as  many  men  hit 
as  there  are  hits  per  area  of  each  assumed  target  (men  standing, 
kneeling,  or  lying  down),  but  it  is  probable  that  this  number  will  be 
smaller,  or,  in  other  words,  even  if  the  target  is  covered  with  the 
proper  density  of  fire  of  one  hit  per  unit  surface,  it  is  not  likely, 
owing  to  irregular  distribution,  that  each  unit  of  surface  will  be 
struck;  the  fraction  x  is,  therefore,  less  than  unity. 

Gen.  Rohne,  of  the  German  field  artillery,  has  discussed  in  his 
essay  on  shrapnel  fire,  the  determination  of  the  fraction,  x,  for  any 
assumed  case.  He  states: 

"It  remains  to  be  shown  how,  and  why,  the  probable  number  of 
men  hit  is  arrived  at.  So  far  as  the  effect  goes,  it  is  evidently  imma- 
terial whether  one  shrapnel  with  600  balls  or  six  shrapnel  with  100 
balls  each,  burst  on  the  target,  supposing  always  that  in  each  case 
the  angle  of  opening,  the  point  of  burst  and  the  angle  of 
descent  are  the  same,  and  that  in  both  cases  the  distri- 
bution of  the  balls  within  the  zone  of  effect  is  the  same.  In  a  like 
manner,  under  the  same  conditions,  it  is  quite  immaterial  whether 
20  hits  result  from  1  round,  or  whether  the  effect  is  produced  by  20 
rounds  of  which  each  makes  1  hit.  We  may  thus  say  that  the  effect 
of  1  round  which  gives  n  hits  is  the  same  as  that  of  n  rounds  which 
give  1  hit  each." 

If  then  we  make  ra  equal  1,  z=Qand  the  expression,  Q(l  —  (1—  x)n) 

becomes,  Q(l-^rr^' 

Assuming  that  30  men  stand  within  the  cone  of  dispersion  and 
that  one  round  gives  20  hits,  the  effect  is  the  same  as  if  20  rounds 

29 
produced  1  hit  each.     We  may  therefore  write  30(1  —  (o>.)20)  =  14.8, 

which  is  49.3  per  cent  of  30,  and  which  corresponds  to  £=0.493  for 

96609°—  11  -  5 


66  GUNNERY  AND  EXPLOSIVES. 

n=l,  thus,  Q(l-(l-^)n)  becomes  30(1-0.507),  or  14.8,  instead  of 
20  for  the  first  round  under  the  assumed  condition! 

29 
If  it  be  assumed  that  1  round  gives  100  hits,  30(1  -(^g)100) =28. 99 

and  £=0.966  for  n=l. 

That  all  the  men  standing  in  the  cone  of  dispersion  are  not  killed 
with  1  round  is  the  assumption  upon  which  the  method  is  based;  x 
is  always  less  than  unity. 

After  x  is  calculated  it  is  of  little  importance  whether  any  single 
round  of  a  group  under  analysis  give  somewhat  more  or  somewhat 
less  than  its  proper  theoretical  percentage  of  killed.  The  general 
result  can  not  be  materially  affected;  if  fewer  are  killed  in  the  first 
round,  more  will  be  killed  in  the  second,  and  so  on. 

68.  Application   of  the   formula. — Suppose  it  is  desired  to 
determine  the  number  of  rounds  necessary  to  put  out  of  action  a 
certain  portion,  z  per  cent,  of  the  target.     The  expressions  given  in 
paragraph  66  assume  that  the  first  round  will  hit  x  per  cent  of  the 
target,  and  that  after  n  rounds  there  remains  (1—  x)n  per  cent  of  the 
target  not  hit.     Introducing  the  condition  that  z  per  cent  is  to  be  hit 

(1—  x)n  must  equal  1—2 

from  which  n=  ° ^)   ~  ; 
log{l-aO 

logri=log.  log.(l-z)-log.  log.(l-z). 

The  information  contained  in  Chapter  VIII  and  up  to  this  point 
in  the  present  chapter  is  sufficient  to  enable  the  student  to  solve, 
theoretically,  the  most  important  problems  in  shrapnel  fire.  It  is 
not  the  purpose  of  this  volume  to  consider  anything  more  than  the 
principles  underlying  the  subject  of  field  artillery  gunnery  and  to 
set  forth  these  principles  in  such  a  way  that  the  officer  of  field  artil- 
lery in  search  of  further  professional  knowledge  may  be  directed 
along  the  proper  lines.  A  knowledge  of  the  theories  upon  which 
practice  is  based  will  in  many  cases  be  of  exceptional  interest  in  the 
analysis  of  practice  firing. 

69.  Dispersion  of  points  of  burst. — In  the  discussion  which 
has  preceded,  it  has  been  assumed  that  each  shrapnel  burst  at  a  pre- 
scribed distance  in  front  of  the  target.     In  practice,  due  to  irregu- 
larities of  burning  of  the  fuses,  the  extreme  points  of  burst  in  a  group 


GUNNERY  AND  EXPLOSIVES.  67 

fired  at  a  range  of  5,000  yards  are  about  90  yards  apart.  The  3 -mil 
height  at  a  range  of  5,000  yards  corresponds  to  a  burst  interval  of 
48  yards,  hence  when  firing  a  group  of  shrapnel  at  this  range  with 
mean  height  of  burst  of  3  mils  there  should  be  no  grazes.  The 
nearest  burst  should  occur  at  3  yards  in  front  of  the  target  and  the 
most  remote  at  93  yards  in  front.  At  shorter  ranges  the  interval  of 
burst  is  greater,  hence  a  burst  on  graze  may  usually  be  attributed 
to  errors  in  laying  and  fuse  setting. 

70.  The  corrector. — The  rate  of  burning  of  different  fuses  of 
the  same  lot  will  be  found  to  be  fairly  uniform,  though  it  will  probably 
vary  slightly  from  that  upon  which  the  fuse  setter  range-ring  scale 
is  based. 

Before  considering  the  function  of  the  corrector,  let  it  be  supposed 
that  a  fuse  setter,  without  corrector,  is  being  used  and  that  fire  is 
being  conducted  with  the  type  lot  of  fuses,  upon  the  behavior 
of  which  the  fuse  setter  range-ring  scale  is  based.  If,  for  instance, 
the  target  is  on  the  same  horizontal  plane  as  the  guns,  it  will  be 
found  that,  neglecting  the  inherent  errors  of  the  fuse  and  assuming 
normal  atmospheric  conditions,  the  shrapnel  bursts  will  be  seen 
in  the  horizontal  plane  through  the  gun ;  in  other  words,  no  matter 
what  the  range  may  be,  the  fuse  will  act  at  the  end  of  that  range 
under  the  conditions  assumed.  If  the  target  and  gun  are  not  on 
the  same  level,  and  the  gun  is  given  an  angle  of  site  elevation  in 
addition  to  the  elevation  for  range,  the  shrapnel  burst  will  occur 
in  a  plane  containing  the  gun  and  target  and  perpendicular  to  the 
plane  of  fire;  this  would  follow  from  a  consideration  of  the  theory 
of  the  rigidity  of  the  trajectory.  Due  to  fuse  errors  the  bursts, 
even  with  the  type  lot,  will  not  occur  precisely  in  the  plane  in 
question,  but  above  and  below  it  in  equal  numbers. 

With  other  lots  of  fuses,  the  majority  of  bursts,  due  to  a  probable 
variation  in  rate  of  burning  from  the  type  lot,  will  occur  below 
or  above  the  plane,  depending  upon  whether  the  time  of  burning 
is  too  long  or  too  short  as  compared  with  the  type  lot. 

The  fuse  setter  was  so  constructed  that  corrector  27  would  put 
the  bursts  in  the  plane  for  the  type  lot  of  fuses  under  normal  con- 
ditions. As  each  division  of  the  corrector  graduations  corresponds 
to  a  change  in  the  height  of  burst  of  the  shrapnel  equal  to  one  one- 
thousandth  of  the  range — that  is,  to  1  mil — it  will  be  seen  that 
the  division  30  corresponds  to  the  normal  height  of  burst  (3  mils) 
for  fire  for  effect,  if  all  conditions  are  normal. 


68  GUNNERY  AND  EXPLOSIVES. 

In  case  the  fuses  of  any  lot  burn  longer  than  those  of  the  type 
lot,  corrector  27  would  not  correspond  to  a  burst  in  the  plane  through 
gun  and  target.  The  corrector  would  have  to  be  increased  by  a 
number  of  points  equal  to  the  number  of  mils  beneath  the  plane 
at  which  the  shrapnel  were  bursting.  If,  for  instance,  the  sense 
of  the  bursts  was  4  mils  below,  the  corrector  should  be  raised  to 
31  for  bursts  in  the  plane  and  to  32  for  the  prescribed  1  mil  height 
of  burst  for  fire  for  adjustment. 

Having  determined  the  corrector  corresponding  to  bursts  in  the 
plane  through  gun  and  target  and  perpendicular  to  the  plane  of 
fire,  as  long  as  atmospheric  conditions  are  normal  no  further  manip- 
ulation is  necessary  except  the  proper  increase  for  firing  for  effect, 
no  matter  wThat  the  range  may  be. 

If,  however,  atmospheric  conditions  are  not  normal,  an  altera- 
tion in  the  corrector  setting  will  be  necessary.  The  corrector  will 
perhaps  vary  at  different  ranges;  usually,  however,  this  variation 
for  any  probable  set  of  conditions  will  be  very  small.  Hence  it  may 
be  stated  as  a  practical  working  rule  that  the  corrector  for  one  range 
is  good  for  all. 

This  rule  works  satisfactorily  for  the  changes  of  range  used  in 
bracketing,  and  also  generally  for  greater  changes  of  range  in  shift- 
ing to  a  new  target,  although  in  the  latter  case  a  slight  readjustment 
of  the  corrector  may  be  required. 


CHAPTER  X. 
RANGING. 

71.  General  considerations. — Ranging  is  the  most  difficult  as 
well  as  the  most  important  part  of  the  adjustment  of  fire.     Skillful 
ranging  at  difficult  targets  requires  a  great  deal  of  practice  in  observ- 
ing the  bursts  of  projectiles. 

From  the  nature  of  its  service,  field  artillery  can  not  have  the 
stationary  appliances  of  the  coast  artillery  for  determining  ranges 
accurately  and  for  making  allowances  for  all  conditions  of  wind, 
barometer,  etc.  Furthermore,  the  shrapnel  is  its  principal  pro- 
jectile and  the  hitting  of  a  bull's  eye  is  not  to  be  sought. 

72.  Methods  of  procedure. — For  the  field  artillery  the  process 
of  ranging  is  one  of  trial  shots  and  the  method  of  procedure  for  a 
battery  is  as  follows: 

The  captain  first  observes  the  target  and  estimates  the  distance  of 
it  from  his  guns.  This  estimate  may  be  made  with  the  eye  or  by 
the  aid  of  a  portable  range  finder.  He  then  fires  at  the  estimated 
range  and  observes  whether  the  projectiles  burst  short  of  or  beyond 
the  target. 

Supposing  the  bursts  to  have  been  short  of  the  target,  he  next 
fires  a  round  with  increased  range,  the  amount  of  increase  being 
such  as  will  probably  include  the  sum  total  of  all  of  the  range  errors 
of  the  gun  and  ammunition,  and  of  the  personnel,  including  the 
error  that  has  been  made  in  estimation  of  the  distance  to  the  target. 

If  this  second  round  is  over,  a  bracket  is  said  to  be  established; 
any  other  trial  ranges  which  he  will  need  to  use  will  be  included 
within  the  limits  of  this  bracket. 

The  most  logical  range  for  him  to  use  for  his  third  trial  is  the  one 
midway  between  the  first  two,  since,  whether  the  third  round  be 
short  or  over,  he  will  have  eliminated  the  ranges  in  one-half  of  the 
bracket  from  the  necessity  for  further  trial. 

He  continues  to  halve  the  bracket  last  obtained  until  he  has  nar- 
rowed it  down  to  the  needs  of  the  case,  but  he  should  never  try  to 
get  a  bracket  smaller  than  the  error  of  his  guns. 


70  GUNNERY  AND  EXPLOSIVES. 

Having  obtained  the  desired  bracket,  he  then  verifies  it  by  firing 
a  sufficient  number  of  rounds  at  the  short  and  long  limits.  A  single 
round  is  never  to  be  trusted  for  deciding  a  short  or  an  over  which 
is  near  the  target,  since  that  one  round  may  be  an  abnormal  one, 
and  the  waste  of  ammunition  which  would  result  from  firing  for 
effect  with  the  erroneous  data  thus  obtained  will,  in  the  end,  more 
than  equal  the  expenditure  required  to  verify  the  bracket.  Fur- 
thermore, the  time  lost  in  firing  at  an  erroneous  range  before  the 
error  is  discovered  can  not  be  replaced. 

A  battery  salvo  is  generally  sufficient  to  verify  each  limit  of  the 
bracket.  If,  during  the  bracketing  process,  any  of  the  rounds  be 
observed  to  produce  effect  upon  the  target,  the  captain  may  abandon 
his  bracketing  process  for  the  time  being  and  fire  additional  rounds 
at  the  same  range.  If  these  rounds  do  not  indicate  that  the  range 
has  been  found,  he  proceeds  with  the  bracketing. 

The  amount  of  increase  of  the  range  for  the  second  trial  round  is 
laid  down  in  Drill  Regulations  as  400  yards.  This  has  been  fixed 
upon  as  the  result  of  much  experience,  as  the  amount  necessary  to 
cover  all  probable  range  errors.  It  is  also  a  number  which  is  readily 
subdivided  several  times  without  giving  a  quotient  which  is  not  an 
even  division  on  the  scales. 

73.  Exceptions  to  the  rule. — The  drill  book  purposely  allows 
exceptions  from  this  rule  to  fit  special  cases;  but  the  beginner  is 
prone  to  apply  the  exception  far  too  frequently,  thinking  that  he 
can  tell  something  about  the  amount  that  his  first  round  is  over  or 
short. 

With  air  bursts  which  obscure  the  target  or  against  which  the  tar- 
get is  silhouetted,  it  is  impossible  for  an  observer  near  the  guns  to 
form  an  estimate  of  how  much  the  point  of  burst  is  short  of  or  beyond 
the  target. 

With  percussion  bursts  it  is  equally  impossible,  except  when  the 
burst  is  very  near  the  target  or  when  the  observer  is  specially  fa- 
vored by  conditions. 

With  percussion  projectiles  the  distance  of  the  point  of  burst  from 
the  target  is  largely  influenced  by  the  contour  of  the  ground. 

Let  us  suppose  that  the  observer  is  on  high  ground  and  that  the 
target  is  on  perfectly  level  ground  below  him  (fig.  12). 

This  would  be  a  special  case  in  which  the  observer  would  be 
justified  in  forming  an  estimate  of  the  amount  that  a  percussion 
burst  was  over  or  short. 


GUNNERY  AND  EXPLOSIVES. 


71 


Let  us  take  the  opposite  extreme  where  the  target  is  on  a  vertical 
surface  (fig.  13).  The  actual  distance  that  the  percussion  hit  is 
short  of  the  target  is  evidently  no  measure  of  the  amount  of  increase 
of  range  required  to  reach  the  target. 

The  normal  target  will  be  in  a  situation  which  lies  between  the 
two  just  illustrated;  that  is,  the  ground  about  it  will  slope  more  or 
less. 


(Tig.  IZ) 


r 


Suppose  that  a  percussion  hit  is  seen  to  be  short  at  a  (fig.  14).  It 
is  evident  that  if  the  ground  had  been  level  the  shot  would  have 
struck  at  b  and  therefore  that  bTis  the  increase  of  range  required  to 
reach  the  target  and  not  aT. 

Even  the  report  of  an  auxiliary  observing  party  on  the  flank  to 
the  effect  that  the  round  struck  100  yards  short,  would  be  of  little 
value  in  this  case. 


If  a  shot  struck  at  a'  the  actual  decrease  in  range  required  would 
be  6' T  and  not  a'T. 

Now,  take  the  case  where  the  target  is  behind  a  crest  (fig.  15). 
If  a  percussion  hit  were  at  a  it  would  probably  not  be  seen  at  all 
from  the  guns  but  an  observing  party  on  the  flank  might  report  it 
400  yards  over,  whereas  the  range  for  the  next  round  needs  to  be 
decreased  only  by  the  distance  Tb. 


72 


GUNNERY  AND  EXPLOSIVES. 


As  this  last  situation  and  the  preceding  one  are  the  usual  ones  for 
targets,  it  will  be  seen  that  the  observer  at  the  guns  is  able  to  tell 
very  little  about  how  much  a  burst  is  over  or  short.  He  should, 
therefore,  stick  closely  to  the  rule  of  changing  his  range  400  yards- for 
the  second  round,  even  when  assisted  by  reports  from  an  auxiliary 
observing  party. 


In  the  examination  of  target  records  officers  frequently  demand  an 
explanation  when,  the  range  set  on  the  sights  having  been  increased 
400  yards,  the  change  in  the  burst  interval  did  not  even  approxi- 
mately correspond.  It  will  be  seen  from  the  above  that  it  should  not 
correspond  except  when  the  target  is  on  level  ground  whose  plane 
passes  through  the  guns. 


(fij.  /S) 


From  the  above  we  might  deduce  the  principle  that  for  percussion 
hits  on  ground  sloping  toward  the  guns  the  burst  interval  will  be  less 
than  the  change  of  range  required  to  hit  the  target,  and  that ^f or  per- 
cussion hits  on  ground  sloping  away  from  the  guns  the  burst  interval 
will  be  greater  than  the  required  change  of  range. 

As  these  slopes  are  seldom  regular,  perhaps  it  would  be  better  to 
make  the  deduction  that  not  much  can  be  told  by  the  observer  as  to 


GUNNERY  AND  EXPLOSIVES.  73 

the  amount  of  the  over  or  short;  he  should  be  satisfied  if  he  ja  able  to 
say  that  he  is  surely  over  or  that  he  is  surely  short. 

Beginners  should  always  follow  the  rule  of  the  400-yards  change. 
They  will  be  surprised  at  the  number  of  times  it  will  keep  them  out 
of  difficulties. 

74.  Ranging  by  time  bursts. — Ranging  by  means  of  percussion 
projectiles  is  often  very  difficult  on  account  of  lost  rounds. 

One  of  the  most  annoying  things  is  a  deep  ravine  in  front  of  the 
target,  whose  existence  has  not  been  discovered.  Rounds  falling  into 
such  a  ravine  may  be  sensed  as  over,  either  because  they  are  not  seen 
at  all  or  because  the  smoke,  when  it  does  rise  into  the  view,  is  so  thin 
that  the  target  is  seen  through  it  and  judged  to  be  in  front  of  it. 

Another  cause  of  lost  rounds  with  percussion  fire  is  soft,  marshy 
ground  which  swallows  up  the  projectiles,  while  still  another  is 
ground  covered  with  dense  brush  or  tropical  growth  which  imprisons 
the  smoke. 

If  the  first  rounds  fired  are  lost  the  battery  commander  is  all  at  sea, 
and  if  he  sticks  to  percussion  fire  has  to  feel  aimlessly  about  until  he 
gets  a  burst  that  can  be  seen. 

Until  the  adoption  of  the  present  fuse  setter  ranging  was  habitually 
done  with  percussion  projectiles,  but  that  instrument  supplies  a 
ready  means  for  avoiding  the  pitfalls  of  percussion  ranging. 

The  theoretical  effect  of  the  fuse  setter  is  to  place  all  of  the  bursts 
in  a  plane  passing  through  the  gun  and  the  target  and  normal  to  the 
plane  of  fire.  In  this  discussion  this  plane  will  be  called  the  zero 
plane.  The  corrector  furnishes  means  of  adjusting  the  heights  of 
burst  so  as  to  bring  them  into  this  plane,  if  conditions  are  not  normal, 
or  to  any  desired  distance  above  such  plane  for  ranging  or  for  fire 
for  effect.  The  theoretical  result  of  placing  the  burst  in  this  plane 
for  ranging  is  that  the  bursts  Appear,  relatively  to  the  target,  as 
percussion  bursts  would  appear  if  the  'target  and  guns  were  on  level 
ground.  The  distances  of  the  bursts  from  the  target  are  then  quite 
independent  of  the  actual  form  of  the  ground. 

This  system  is  practicable  only  with  a  fuse  which  burns  with 
reasonable  regularity,  and  a  fuse  setter  in  which  the  setting  is  always 
that  due  to  the  range,  modified  by  the  corrector  for  the  various 
conditions  of  the  firing. 

While  theoretically  the  effect  of  the  fuse  setter  is  to  place  all  of  the 
bursts  in  one  plane,  it  will  be  readily  understood  that  in  practice 
many  bursts  will  be  a  little  above  or  below  this  plane.  The  mean 


74  GUNNERY  AND  EXPLOSIVES. 

point  of  burst  of  a  series  of  shrapnel  can,  however,  be  brought  into 
this  plane.  If  the  average  variation  of  the  fuse  is  small,  the  smoke 
of  burst,  spreading  out  in  all  directions  from  the  bursting  point,  will 
conceal  the  target,  or  the  target  will  appear  silhouetted  against  it  if 
th^  direction  is  properly  adjusted.  Moreover  all  bursts,  whether  air 
or  percussion,  that  appear  below  a  target  which  is  on  a  crest  are 
manifestly  short.  The  only  rounds  which  the  observer  may  not 
judge  as  short  or  over  are  those  bursting  so  high  that  no  portion  of  the 
smoke  ball  reaches  down  to  the  target. 

As  the  bracket  is  narrowed  down  and  the  bursts  occur  near  the 
target  a  certain  proportion  of  the  bursts  will  be  on  graze,  due  to  the 
fact  that  the  ground  approaches  the  zero  plane  at  this  point;  any 
irregularities  of  burst  cause  a  certain  percentage  of  the  fuses  to  burst 
below  the  plane. 

Percussion  bursts  may  also  occur  at  other  points  along  the  range 
where  the  ground  is  near  to  or  above  the  zero  plane;  unless  such 
percussion  hits  bracket  the  target  they  do  not  indicate  that  the 
proper  range  has  been  obtained. 

75.  Height  of  burst  for  ranging. — In  practice,  time  bursts 
for  ranging  are  placed  above  the  zero  plane,  so  ihat  they  will  appear 
at  a  height  of  one  mil  above  the  target  as  seen  from  a  point  near  the 
guns. 

The  adoption  of  the  one-mil  height  of  burst  of  fuses  during  the 
ranging  process  is  based  upon  the  following  analysis:  To  assist  obser- 
vation the  smoke  ball  must  be  silhouetted  against  or  silhouetted  by 
the  target;  at  short  and  medium  ranges  the  one-mil  height  is  admira- 
bly suited  to  such  purpose,  as  the  diameter  of  the  smoke  ball  imme- 
diately after  the  time  burst  is  about  4  yards.  At  long  ranges  the  one- 
mil  height  of  burst  is  theoretically  too  large.  An  incident  to  the 
practice  of  using  the  one-mil  height  of  burst  in  ranging  is  the  resulting 
shrapnel  effect. 

For  short  and  medium  ranges  this  slight  elevation  of  the  bursting 
point  does  not  produce  an  undue  percentage  of  bursts  too  high  for 
purposes  of  observation,  but  for  long  ranges  it  may  be  advantageous 
to  use  a  little  lower  corrector,  as  the  one-mil  height  of  burst  at  such 
ranges  corresponds  to  a  greater  distance  above  the  plane;  further- 
more, observation  is  more  difficult  on  account  of  the  distance. 

In  adjusting  the  mean  height  of  burst  to  any  plane  account  must 
be  taken  of  the  percussion  bursts  as  well  as  of  the  air  bursts,  since  the 
percussion  bursts  would  have  been  low-time  bursts  with  the  ground 


GUNNERY  AND  EXPLOSIVES.  75 

out  of  the  way.  The  occurrence  of  an  average  of  one  percussion 
burst  in  four  shots  is  an  indication  that  the  proper  height  of  burst  for 
adjustment  has  been  obtained. 

Estimating  the  mean  height  of  burst  by  observing  only  the  air 
bursts  of  a  group  of  shots  which  also  contains  percussion  hits  is  an 
erroneous  method. 

The  proper  method  of  observing  the  mean  height  of  burst  is  similar 
to  the  method  of  observation  of  the  range.  That  is,  the  observer 
should  endeavor  to  determine  whether  the  mean  point  is  above  or 
below  the  desired  plane.  When  all  of  the  bursts  of  the  group  are  in 
the  air  and  are  closely  grouped,  it  then  becomes  practicable  to  make 
a  good  estimate  of  the  amount  of  correction  necessary. 

If  fuses  are  poor  ranging  with  time  fire  will  be  less  satisfactory, 
but  some  advantage  may  still  be  gained  from  it,  since  with  a  low 
corrector  a  portion  of  time  bursts  will  si  ill  be  seen  and  many  of  the 
lost  rounds  which  would  result  from  percussion  ranging  will  still  be 
avoided. 

Ranging  with  time  fire  has  also  the  advantage  that  during  the 
bracketing  process  the  action  of  the  fuse  is  observed  and  corrected, 
so  that  the  proper  corrector  for  fire  for  effect  will  be  known  as  soon 
as  the  range  is  obtained.  As  time  fire  is  used  for  effect  in  the  majority 
of  cases  this  is  a  considerable  advantage. 

Observations  on  air  bursts  from  auxiliary  stations  on  the  flanks  of 
the  line  of  fire  give  more  reliable  information  than  do  similar  obser- 
vations on  percussion  bursts.  The  location  of  the  percussion  burst 
is,  as  we  have  seen,  dependent  upon  the  form  of  the  ground,  whereas 
that  of  the  time  burst  is  independent  of  the  form  of  the  ground. 
Furthermore  the  percussion  bursts  are  dependent  upon  the  laying 
of  the  gun  in  elevation.  If,  for  example,  a  gunner  (haying  mis- 
understood the  range)  laid  100  yards  too  high,  the  percussion  burst 
would  be  farther  from  the  gun  than  it  should  be  and,  even  if  the 
firing  were  over  level  ground,  the  burst  interval  reported  by  the 
observing  party  would  not  be  that  due  to  the  range  ordered  at  the 
guns.  If,  on  the  other  hand,  a  time  burst  be  considered,  it  will  be 
seen  that  the  effect  of  the  form  of  the  ground  will  be  eliminated  and 
that  the  effect  of  the  faulty  laying  will  be  to  place  the  burst  higher 
in  the  air,  but  with  the  same  burst  interval  that  it  would  have  had 
if  the  gun  had  been  correctly  laid.  The  burst  interval  reported  will 
be  correct  and  the  gunner's  error  will  be  detected. 


76  GUNNERY  AND  EXPLOSIVES. 

Large  errors  in  fuse  setting  are  rare  and  are  easily  detected,  while 
ordinary  variations  in  setting  are  very  small,  so  that  variations  in 
burst  interval  due  to  the  fuse  are  reduced  nearly  to  the  error  of  the 
fuse  itself. 

The  error  of  the  fuse  now  in  use  is  about  equal  to  the  error  of  the 
gun;  therefore  since  the  error  of  the  gun  and  of  the  gunner  and  the 
influence  of  the  form  of  the  ground  on  the  burst  interval  are  elimi- 
nated in  ranging  with  time  bursts,  the  error  of  the  fuse  only  being 
introduced,  much  better  results  should  be  obtained  from  this  method. 

In  all  ranging  the  officer  conducting  the  fire  should  depend  first 
of  all  on  seeing  whether  the  ball  of  smoke  produced  by  the  bursting 
projectile  is  short  of  or  beyond  the  target. 

There  are  other  means  of  judging  the  range,  such  as  observing  the 
strike  of  shrapnel  case,  noting  the  dust  knocked  up  by  shrapnel 
balls,  etc.  All  such  indications  are  dependent  on  the  conditions 
of  the  ground  about  the  target  and  should  be  considered  only  as 
secondary  matters  to  be  noted  when  it  can  be  done  without  diverting 
the  officer's  attention  from  the  main  reliance. 

Officers  whose  firing  experience  is  confined  to  a  single  firing  ground 
are  prone  to  place  top  much  reliance  on  such  of  these  secondary 
indications  as  are  continually  available  on  that  ground. 


CHAPTER  XI. 

PREPARATION    AND   CONDUCT   OF   FIRE. 

76.  General  remarks. — The  preceding  chapters  have  dealt,  in 
a  simple  manner,  with  the  theory  of  gunnery  as  applied  to  the 
3-inch  field  artillery  materiel.     It  is  assumed  that  the  student  has 
reviewed  the  Drill  Regulations  and  the  handbook.     Even  without 
having  handled  the  plant,  he  should  be  impressed  with  its  power 
and  flexibility  and  the  possibility  of  subordinating  such  weapon  to 
intelligent  control.     It  is  no  small  matter  to  contemplate  the  respon- 
sibility of  conducting  fire  during  times  of  actual  stress,  where  per- 
formances are  almost  wholly  based  upon  previous  instruction  in 
problems  where  such  stress  is  lacking. 

The  officer  conducting  the  fire — and  every  officer  in  an  artillery 
command  should  be  able  to  replace  him — has  no  time  during  stress 
for  reposeful  judicial  action.  He  must  do  something,  do  that  some- 
thing quickly,  and  do  it  right.  For  this  reason  a  proper  training 
and  much  practice  in  time  of  peace  become  most  important  for 
him. 

It  is  not  held  that  all  the  matter  contained  in  the  preceding 
chapters  of  this  volume  is  absolutely  essential  to  the  success  of  an 
individual  field  artillery  commander  in  time  of  war.  It  is  main- 
tained, however,  that  study  of  the  profession  as  here  set  forth  will 
greatly  assist  in  the  understanding  of  the  Drill  Regulations. 

77.  Axioms  in  the  profession. — As  is  the  case  among  leaders 
of  other  professions,  there  are  many  points  upon  which  eminent 
field  artillerymen  disagree.     This  disagreement  is  a  form  of  intel- 
lectual activity,  as  a  result  of  which  acceptable  and  agreeable  pro- 
fessional notions  are  evolved.     These  notions  become  the  profes- 
sional   axioms — the    common   meeting    point — of   all    enthusiastic 
artillerymen  harassed  by  temporary  disagreements  upon  subjects 
less    vitally    important.    The    Drill    Regulations    are    constructed 
about  the  professional  axioms.     In  particular,  the  pages  on  prepa- 
ration and  conduct  of  fire  and  those  concerning  artillery  in  the 
field  should  be  analyzed  most  closely.     Fire  action  is  the  only  thing 
that  justifies  the  existence  of  the  arm. 

(a)  One  of  the  first  requirements  is  to  occupy  a  position 
without  the  knowledge  of  the  enemy;  opening  fire  should 
surprise  him. — It  is  almost  impossible  to  measure  the  importance 

77 


78  GUNNERY  AND  EXPLOSIVES. 

of  this  requirement.  In  a  position  not  yet  revealed  to  the  enemy, 
preparations  for  opening  fire  may  be  made  with  a  fair  degree  of  cool- 
ness and  with  great  speed  and  accuracy.  Even  though  it  be  not 
possible  to  provide  for  subsequent  phases  of  the  action,  the  advan- 
tage secured  by  surprising  an  enemy  should  continue  until  the  na- 
ture of  the  problem  is  changed  by  the  introduction  of  other  ele- 
ments. The  history  of  warfare  is  full  of  incidents  illustrating  the 
value  of  action  by  surprise. 

(b)  The  time  from  first  round  to  effective  shrapnel  fire  should 
be  a  minimum. — The  total  time  which  elapses  from  the  instant  of 
firing  the  opening  round  to  the  first  effective  round  is  made  up  of 
several  elements,  as  follows: 

Time  of  flight  of  first  round. 

Time  consumed  in  observation  of  first  round. 

Time  consumed  in  determining,  announcing,  and  applying 
corrections  based  upon  observation  of  first  round. 

Time  consumed  in  bracketing. 

The  officer  conducting  the  fire  has  no  control  over  the  projectile's 
time  of  flight.  In  so  far  as  ranging  is  concerned  this  time  is  lost.  The 
time  consumed  in  observation  of  fire  becomes  more  nearly  a  minimum 
as  he  becomes  more  adept  in  the  use  of  his  plant.  A  careful  study 
of  the  chapter  on  ranging  will  reveal  many  points  of  value  to  an  ob- 
server. Experience,  however,  is  the  only  really  satisfactory  way  to 
acquire  an  aptitude  for  rapid  and  accurate  judgment  in  the  most 
important  art  of  fire  observation. 

The  time  consumed  in  determining  the  corrections  to  be  applied 
before  subsequent  rounds  may  be  delivered  should  be  negligible  in  the 
case  of  officers  even  reasonably  prepared  for  their  duties.  The  paral- 
lax method  is  rapid  as  well  as  simple,  and  a  well-instructed,  con- 
scientious officer  should  feel  humiliated  if  time  were  lost  in  making 
unnecessary  changes. 

In  the  great  majority  of  cases  bracketing  is  necessary;  even  where 
the  initial  round  is  observed  at  the  target,  verifying  rounds  are  neces- 
sary; by  skill  proceeding  from  study,  thoughtful  assimilation  of  the 
fundamentals,  and  above  all  from  experience  may  the  important  time 
from  opening  fire  to  the  first  effective  shrapnel  round  be  reduced  to  a 
minimum. 

(c)  The  expenditure  of  ammunition  in  the  accomplishment 
of  a  given  purpose  should  be  a  minimum. — One  of  the  character- 
istic properties  of  modern  field  artillery  is  rapidity  of  fire.     By  virtue 
of  this  mechanical  function  it  is  possible  to  bring  a  crushing  fire  to 


GUNNERY  AND  EXPLOSIVES.  79 

bear  upon  a  vulnerable  enemy  before  he  can  escape  from  its  action. 
Limiting  the  application  of  rapidity  of  fire  is  the  necessity  for  con- 
serving ammunition,  hence  the  rule  above.  Drill  Regulations  state: 
"It  is  made  the  duty  of  every  field  artillery  commander  to  exercise  constant 
and  unremitting  care  to  economize  ammunition."  The  chapter  on 
ranging  prescribes  methods  by  which  ammunition  may  be  saved 
during  the  preliminaries  to  fire  for  effect.  It  is  possible  to  prescribe 
definite  rules  leading  to  a  fairly  economical  adjustment  of  fire,  but 
when  fire  for  effect  begins  the  officer  conducting  the  fire  alone  can 
compare  his  expenditures  with  the  observed  effect.  As  stated  in 
Chapter  I,  the  limit  of  the  power  of  light  field  artillery  has  been 
reached  when  opposing  personnel  is  being  annihilated,  when  oppos- 
ing materiel  of  like  power  is  being  destroyed  and  when  the  fire  from 
moderately  entrenched  positions  is  being  neutralized.  Generally 
speaking,  the  officer  conducting  the  fire  should  be  guided  in  his 
choice  of  a  method  of  fire  by  the  desirability  of  getting  a  sufficient 
effect  as  quickly  and  as  surely  as  possible.  Fire  should  cease  as  soon 
as  the  desired  effect  is  produced;  the  rate  of  fire  and  therefore  the 
amount  of  ammunition  expended  should  be  commensurate  with  the 
object  to  be  obtained. 

78.  Effect  as  a  function  of  ammunition  expended.  —  Referring 
to  paragraph  68, 

log  (l-z) 

'    log  (l-z) 

in  which  n  is  the  number  of  rounds  necessary  to  put  out  of  action  a 
certain  portion,  z  per  cent,  of  the  target.  Suppose  x  to  equal  0.10; 
then,  in  order  to  put  out  of  action  50  per  cent  of  the  target,  2=0.50 


n--6.57  rounds 
log  0.90 

if  2=0.60  n=  8.5 

z=  .70  w=11.4 

2=  .80  n=15.3 

z=  .90  n=21.8 

It  will  be  seen  that  after  a  certain  number  of  rounds  the  killing 
effect  is  hardly  commensurate  with  the  expenditure  of  ammunition. 
It  may,  however,  be  necessary  to  continue  the  fire  in  order  to  keep  a 
previously  overwhelmed  though  possibly  active  enemy  pinned  to 
the  earth.  The  amount  of  ammunition  to  be  expended  in  the  ac- 
complishment of  a  given  purpose  is  ordinarily  not  capable  of  pre- 
determination; the  officer  conducting  the  fire  must  regulate  it  in 
accordance  with  existing  conditions. 


EXPLOSIVES. 


96609°— 11 6  81 


PART  II.— EXPLOSIVES. 

CHAPTER  I. 
EXPLOSIVES. 

1.  General  remarks. — The  power  due  to  the  action  of  which 
the  projectile  is  propelled  from  the  gun  is  present  in  the  powder 
charge  contained  in  the  cartridge  case. 

This  powder  is  ignited  by  means  of  a  percussion  primer,  is  con- 
verted into  gas,  and  in  the  act  of  expanding  forces  the  projectile 
through  the  bore  of  the  gun  with  a  rapidly  increasing  velocity.  In 
the  case  of  propelling  charges  the  combustion  is  gradual,  gas  being 
evolved  by  the  burning  powder  during  all  or  nearly  all  of  the  time 
of  passage  of  the  projectile  through  the  bore  of  the  gun.  In  the  3-inch 
field  gun  this  time  amounts  to  about  two-tenths  of  a  second,  or  that 
during  which  a  stone  would  fall  about  8  inches  under  the  action  of 
gravity. 

2.  Nature  of  combustion.— The  phenomena  of  combustion  are 
found  variously  illustrated  in  nature.     The  more  noticeable  processes 
in  which  a  combustible  is  combined  with  a  supporter  of  combustion 
are  attended  with  a  production  of  heat  or  light,  or  frequently  both. 
There  are  processes  of  combustion  involving  considerable  time,  as 
an  example,  the  decay  of  a  tree;  such  action  is  as  truly  combustion 
as  is  the  burning  of  gas  or  coal. 

When  the  hydrogen  and  carbon  of  which  combustibles  are  mainly 
formed  are  so  heated  as  to  commence  to  combine  with  atmos- 
pheric oxygen,  the  process  is  a  gradual  one.  The  air  in  the  imme- 
diate vicinity  is  first  utilized,  and  as  the  oxygen  it  contains  is 
expended,  more  rushes  in  until  all  the  hydrogen  is  converted  to 
water,  and  the  carbon  into  carbon  monoxide  and  carbon  dioxide. 

It  should  be  understood,  at  this  point  of  the  discussion,  that  the 
chemical  action  just  described  develops  power.  In  the  case  of  the 
decaying  tree  such  power  may  not  be  utilized,  but  that  contained 
in  coal,  oil,  or  gas  is  subject  to  continuous  industrial  demand. 

83 


84  GUNNERY  AND  EXPLOSIVES. 

3.  Nature  of  an  explosion. — If  by  any  means  the  supply  of 
the  supporter  of  combustion  be  increased,  combustion  is  rendered 
more  rapid  and  consequently  more  violent.     Generally  speaking, 
explosion  may  be  defined  as  a  sudden  and  violent  increase  in  the 
volume  of  a  substance.     Chemically,  explosion  is  the  rapid  conver- 
sion of  a  solid  or  liquid  to  the  gaseous  state,  or  the  instantaneous, 
or  nearly  instantaneous,  combination  of  two  or  more  gases  accom- 
panied by  increase  of  volume. 

Certain  compounds  contain  a  considerable  quantity  of  oxygen, 
with  which  they  are  very  ready  to  part  when  heated,  and  if,  there- 
fore, one  of  these  materials  be  intimately  mixed  with  a  readily  oxi- 
dizable  substance,  it  is  clear  that  combustion  will  be  more  rapid 
than  in  the  case  where  oxygen  must  be  obtained  gradually  from  the 
air.  Explosion  is,  therefore,  produced  by  a  very  rapid  combustion. 

4.  Effect   of  confinement. — If   an   explosive   mixture   or   an 
explosive  compound  be  ignited  and  left  to  burn  in  air,  in  the  usual 
case  an  appreciable  time  will  be  necessary  for  its  combustion.  _  The 
burning  surfaces,  exposed  to  the  air,  will  be  relieved  from  their  hot 
gases  as  soon  as  formed ;  these  burning  gases  will  have  no  tendency  to 
penetrate  the  mass  of  the  explosive,  but  will  blow  away  along  the 
easiest  path. 

If,  however,  such  mixture  or  compound  be  confined  in  a  closed 
vessel  a  high  degree  of  pressure  is  soon  set  up.  This  pressure  increases 
the  rate  of  burning,  the  burning  in  its  turn  increases  the  pressure,  and 
so  on,  the  result  being  that  the  process  of  combustion  is  completed 
in  a  time  almost  inappreciably  small. 

5.  Detonation. — We  have  seen  that  in  the  process  of  combustion 
the  chemical  reaction  takes  place  slowly,  whereas  in  explosion  such 
reaction  occupies  a  smaller  time.     An  explosion  starts  with  the 
explosion  of  a  single  particle  and  takes  place  progressively  from 
particle  to  particle  until  the  phenomenon  is  complete.     Detonation 
is  effected  with  greater  rapidity  than  is  explosion;  apparently  there 
is  no  progression  from  particle  to  particle,  but  an  instantaneous 
conversion  of  all  of  the  explosive  compound  into  gases. 

The  difference  in  the  rapidity  of  reaction  has  given  rise  to  the 
division  of  explosives  into  two  groups,  high  explosives  and  progressive 
explosives.  The  principal  high  explosives  in  general  use  are  nitro- 
glycerin,  the  dynamites,  guncotton,  picric  acid  and  its  salts,  tri- 
nitro-toluol,  and  the  fulminate  of  mercury.  The  various  gunpowders 


GUNNERY  AND  EXPLOSIVES.  85 

are  progressive  explosives.  Gunpowder  is  a  term  covering  charcoal 
and  smokeless  powders  used  as  propellants  in  service  or  sporting 
weapons. 

6.  Charcoal  powders. — The  black  gunpowder  used  as  a  base 
charge  for  shrapnel  and  in  the  preparation  of  igniters  is  a  mechanical 
mixture  of  niter  (potassium  nitrate),  charcoal,  and  sulphur  in  the 
proportions,  approximately,  of  75  parts  niter,  15  charcoal,  and  10 
sulphur.     Niter  furnishes  the  oxygen  in  the  above  mixture  and 
charcoal  is  the  combustible;  sulphur  is  used  in  gunpowder  to  lower 
the  point  of  ignition  of  the  mixture  and  to  give  density  to  the  grain. 

In  the  manufacture  of  black  powder  the  ingredients  are  intimately 
mixed,  incorporation  taking  place  in  a  wheel  mill,  under  heavy  iron 
rollers.  A  cake  is  formed  by  pressing,  then  broken  up  into  grains. 
The  grains  are  rumbled  in  wooden  barrels  where  they  are  glazed, 
either  alone  or  with  a  small  quantity  of  graphite.  The  powder  is 
thoroughly  blended  to  overcome  as  far  as  possible  irregularities  in 
manufacture. 

Black  meal  powder  used  in  the  manufacture  of  time  trains  for 
fuses  is  a  charcoal  powder,  usually  of  slightly  different  percentages 
of  niter,  sulphur,  and  charcoal,  and  in  some  cases  containing  a 
slowing  ingredient  as,  for  instance,  barium  nitrate. 

7.  Smokeless   powders. — There  are  two  classes  of  smokeless 
powders  used  in  our  service,  nitro-glycerin  powder  and  nitrocellu- 
lose powder. 

Both  classes  of  powders  are  made  from  guncotton.  The  nitro- 
glycerin  powder  is  so  called  from  the  fact  that  it  contains  a  certain 
amount  of  nitro-glycerin — in  our  small-arms  powder  about  30  per 
cent  by  weight.  The  principal  merit  of  smokeless  powder  is,  of 
course,  its  invisibility,  such  advantage  more  than  counterbalancing 
its  increased  cost  and  time  consuming  complexities  of  manufacture. 
The  length  of  time  required  for  the  drying  of  guncotton  powders  has 
caused  much  concern.  In  time  of  war  this  operation  would  greatly 
retard  the  output  of  powder. 

The  materials  and  processes  employed  in  the  manufacture  of  smoke- 
less powder  are  prescribed  by  the  Ordnance  Department  in  rigid 
specifications,  and  the  manufacture  in  all  its  stages  is  under  careful 
inspection.  The  proof  of  the  powder  consists  of  tests  made  to  deter- 
mine its  ballistic  qualities,  its  uniformity,  and  its  stability  under 
various  conditions.  In  the  3-inch  field  gun  a  muzzle  velocity  of 


86  GUNNERY  AND  EXPLOSIVES. 

1,700  feet  per  second  must  be  obtained  with  a  pressure  not  exceeding, 
approximately,  30,000  pounds  per  square  inch;  the  extreme  varia- 
tion in  velocity  must  not  exceed  1  per  cent  of  the  required  velocity. 

8.  Form  and  size  of  grains. — The  most  desirable  form  of  powder 
grain  is  one  which  gives  off  gas  slowly  at  first,  starting  the  projectile 
before  a  high  pressure  is  reached,  and  then  with  an  increased  burn- 
ing surface  and  a  more  rapid  evolution  of  gas  maintaining  the  pressure 
behind  the  projectile  as  it  moves  down  the  bore.  Carrying  out  this 
idea  of  a  proper  grain,  the  cannon  powder  in  our  service  is  formed  into 
cylindrical  grains  with  seven  longitudinal  perforations,  one  central 
and  the  other  six  equally  distributed  midway  between  the  center  of 
the  grain  and  its  circumference.  In  other  services  cannon  powders 
are  made  into  grains  of  various  shapes.  Cubes,  solid  and  tubular 
rods  of  circular  cross  section,  flat  strips,  and  rolled  sheets  are  among 
other  practicable  forms.1 

Generally  speaking,  the  length  and  diameter  of  the  grain  vary  in 
powders  for  different  guns,  the  size  increasing  with  the  caliber  of 
the  gun.  It  has  been  found  that  the  rate  of  burning  of  powders  is 
affected  by  their  density;  this  principle  is  utilized  in  the  manufac- 
ture of  time  trains  for  fuses  and  in  delay  action  primers.  In  outlin- 
ing the  progress  in  the  manufacture  of  gunpowders  and  the  develop- 
ment of  the  fundamental  principles  upon  which  our  service  powders 
are  designed,  Maj.  Lissak  (Ord.  Dept.,  U.  S.  A.,  retired)  states  essen- 
tially : 

'  'No  marked  improvement  was  made  in  gunpowder  until  1860,  when 
the  principle  of  progressive  combustion  of  powder  was  discovered,  and 
that  the  rate  of  combustion,  and  consequently  the  pressure  exerted 
in  the  gun,  could  be  controlled  by  compressing  the  fine  grained 
powder  previously  used  into  larger  grains  of  greater  density.  The 
rate  or  velocity  of  combustion  was  found  to  diminish  as  the  density 
of  the  powder  increased.  The  increase  in  size  of  grain  diminished 
the  surface  inflamed,  and  the  increased  density  diminished  the  rate 
of  combustion,  so  that,  in  the  new  form,  the  powder  evolved  less  gas 
in  the  first  instants  of  combustion,  and  the  evolution  of  gas  con- 
tinued as  the  projectile  moved  through  the  bore.  By  these  means 
higher  muzzle  velocities  were  obtained  with  lower  maximum  pres- 
sures. To  obtain  a  progressively  increasing  surface  the  perforated 

i  For  computations  concerning  the  action  of  various  forms  of  powder  grains,  see 
issak's  Ordnance  and  Gunnery  (John  Wiley  &  Sons,  1907). 


Lissak 


GUNNERY  AND  EXPLOSIVES.  87 

grain  was  proposed,  and  the  prismatic  form  as  the  most  convenient 
for  building  into  charges.  Powder  was  thereafter  made  into  grains 
of  size  suitable  to  the  gun  for  which  intended,  small  grained  powder 
for  guns  of  small  caliber,  and  large  grained  powder  for  the  larger  guns, 
the  powders  of  regular  granulation,  such  as  the  cubical,  hexagonal 
and  sphero-hexagonal,  came  into  use,  and  finally  for  the  larger  guns 
the  prismatic  powder  in  the  form  of  perforated  hexagonal  prisms. 
*  *  *  A  still  further  advance  in  the  improvement  of  powders 
was  brought  about  in  1886  by  the  introduction  of  smokeless  powders. 
These  powders  are  chemical  compounds  and  not  mechanical  mixtures 
like  the  charcoal  powders;  they  burn  more  slowly  than  the  char- 
coal powders  and  produce  practically  no  smoke." 

The  grain  used  in  the  3-inch  field  gun  is  a  cylindrical,  multiper- 
f orated  grain  about  f-inch  long  and  J-inch  wide.  A  description  of 
the  service  powder  charge  will  be  found  in  the  handbook. 

9.  Manufacture  of  smokeless  powders. — As  stated  previously, 
military  powder  is  usually  one  of  two  general  types — nitrocellulose 
or  nitroglycerin  powder.  In  this  country  the  nitrocellulose  pow- 
ders have  been  adopted  for  cannon;  in  foreign  countries  both  kinds 
are  used;  in  England,  for*  instance,  cordite,  a  nitoglycerin  powder, 
is  the  principal  propellant.  Generally  speaking,  the  manufacture 
of  either  of  the  two  classes  of  smokeless  powders  involves  the  same 
functions,  i.  e.,  that  of  nitrating  some  supporter  of  combustion  and 
forming  the  resulting  substance  into  grains  properly  designed  for 
the  weapon  for  which  intended.  In  nitrocellulose  powder  short 
cotton  fiber  furnishes  the  carbon  or  combustible,  whereas  glycerin 
furnishes  a  part  of  the  -  combustible  in  the  nitroglycerin  powders. 
Guncotton  or  nitrocellulose  is  formed  by  acting  upon  cotton  with 
nitric  and  sulphuric  acid;  the  function  of  the  latter  acid  is  to  com- 
bine with  such  water  as  might  otherwise  dilute  the  nitric  acid,  thus 
preventing  the  proper  nitration  of  the  cotton.  The  nitrated  cotton 
is  then  placed  in  a  solvent  (usually  ether-alcohol  or  acetone),  by 
which  process  it  is  colloided  or  formed  into  a  tough  horny  mass. 
The  colloid  is  pressed  through  dies  containing  pins,  which  form  the 
perforations  in  the  powder  grain.  The  colloid  comes  through  the 
dies  in  long  strings,  having  the  appearance  of  macaroni ;  these  strings 
are  cut  up  into  grains  which  are  sent  through  a  process  for  removing 
and  recovering  the  solvent.  After  drying  to  a  certain  standard  a  lot 
is  ready  for  proof ;  such  proof  consists  in  an  inspection  of  the  physical 
dimensions  of  the  grain — length,  diameter,  thickness  of  web,  density, 


88  GUNNERY  AND  EXPLOSIVES. 

strength  to  resist  compresssion — as  well  as  firing  tests  to  determine 
its  velocity  for  certain  pressures  and  charges,  and  a  laboratory  test 
to  determine  its  composition  and  probable  behavior  in  storage. 

10.  Flashless  powders.— In  recent  years  the  belief  has  grown 
that  military  powders  should  be  not  only  smokeless  but  flashless  as 
well,  so  as  not  to  disclose  the  position  of  a  firing  unit.     The  ordinary 
forms  of  smokeless  powders  are  not  usually  flashless.     Smokeless 
powder  has  a  very  high  temperature  of  explosion,  and  when  the 
projectile  leaves  the  gun  the  strong  luminous  flash,  together  with 
unburnt  slivers  of  powder  coming  out  with  the  blast,  are  clearly 
visible  for  great  distances.     The  problem  has  been  fairly  well  solved ; 
the   Field  Artillery  Board  has  experimented   with  a  reasonably 
satisfactory  flashless  powder,  and,  comparing  its  visibility  with  that 
of  service  powders,  has  recommended : 

(a)  That  the  present  service  powder  has  a  flash  of  such  brilliance 
as  to  make  dismounted  and  mounted  defilade  practically  useless 
so  far  as  concealment  is  concerned. 

(6)  That  if  flashless  powders  can  be  made  to  give  as  good  ballistic 
results  as  the  service  powders  they  are  to  be  preferred. 

It  is  believed  that  before  long  the  service  will  be  supplied  with  a 
powder  quite  as  good  ballistically  as  the  present  powder  and  at  the 
same  time  practically  flashless. 

11.  Other  progressive  powders. — The  manufacture  of  military 
powders  has  had  no  easy  problem  to  solve;  the  nitrocellulose  and 
nitroglycerin  powders  have  been  not  altogether  satisfactory,  in  that 
their  stability  is  not  beyond  question,  except  for  comparatively  short 
periods  of  time  and  under  good  storage  conditions.     By  extreme 
care  the  manufacturing  processes  have  been  brought  to  a  great 
degree  of  refinement;  investigation  has  led  to  the  adoption  of  certain 
stabilizers  or  indicators  of  stability ;  fundamentally,  however,  there 
are  objections  to  the  use  of  nitrocellulose  for  service  powders.     This 
material  is  complex,  and  therefore  liable  to  form  unstable  compounds; 
under  the  influence  of  heat  and  moisture  the  nitrocellulose  is  most 
apt  to  decompose.    The  question  of  a  war  reserve  of  powders,  based 
upon  nitrocotton  or  nitroglycerin,  is  limited   by   their  tendency 
to  deteriorate,  whereas  the  problem  of  supplying  such  powders  in 
times  of  stress  is  greatly  affected  by  the  time  consumed  in  manufac- 
ture and  drying.     Manufacturers,'  inventors,  and  powder  experts 
have  been,  and  are  now,  engaged  in  solving  tne  problem  of  military 


GUNNERY  AND  EXPLOSIVES.  89 

powders;  almost  every  supporter  of  combustion  has  been  variously 
combined  with  different  combustibles  in  the  hope  of  ultimately  dis- 
covering a  proper  powder. 

12.  Firing  a  field  gun. — When  the  percussion  primer  in  the 
base  of  the  cartridge  case  is  fired  a  flame  is  shot  into  the  propelling 
charge.  This  flame,  assisted  by  a  small  charge  of  black  rifle  powder 
placed  in  front  of  the  propelling  charge,  causes  ignition  of  the  powder 
grains.  As  gas  is  evolved  the  pressure  rises  until  it  becomes  sufficient 
to  move  the  projectile  against  the  resistance  of  the  rifling;  the 
projectile  begins  to  move,  and  its  motion  is  accelerated  by  the 
pressure  of  the  increasing  and  expanding  powder  gases  until  a 
maximum  speed  is  attained  at  or  near  the  muzzle. 


CHAPTER  II. 

HIGH    EXPLOSIVES. 

13.  General  considerations. — It  has  been  seen  that  the  special 
purpose  of  the  3-inch  field  gun  is  attack  on  personnel.     Where, 
however,  such  personnel  is  protected  by  overhead  and  head  cover, 
it  must  be  exposed  before  it  can  be  affected  by  the  shrapnel  balls. 
For  the  destruction  of  walls,  parapets,  and  other  obstacles  high 
explosives  are  necessary. 

14.  Subdivision  according  to  use. — For  military  purposes  high 
explosives  are  used  to  produce  demolitions: 

(a)  At  relatively  long  distances  from  our  troops;  the  material  to  be 
destroyed  being  in  the  actual  or  probable  possession  of  the  enemy. 

(6)  Within  our  lines;  the  material  to  be  destroyed  being  in  our 
possession  and  the  destruction  necessary  in  order  to  cause  loss  or 
annoyance  to  the  enemy  or  to  facilitate  our  own  progress. 

In  the  first  case  it  is  usual  to  employ  high  explosive  projectiles, 
delivering  them  at  gun  ranges  for  effect  upon  impact;  in  the  second 
case  it  is  usual  to  carry  the  explosive  to  the  desired  point,  where 
it  is  used  in  accordance  with  methods  set  forth  in  the  Manual  of 
Military  Field  Engineering. 

Except  when  absolutely  necessary,  artillery  must  not  be  used 
for  purposes  of  demolition  other  than  those  in  which  the  object  to 
be  accomplished  is  the  exposure  of  personnel  or  the  destruction  of 
other  artillery. 

15.  Military  high  explosives. — High  explosives  for  military  use 
should  be: 

(a)  Stable  and  not  easily  affected  by  reasonable  variations  of 
temperature  and  moisture;  shell  fillers  should  not  form  unstable 
compounds  (metallic  salts). 

(6)  Insensitive  to  the  usual  shocks  of  transportation;  shell  fillers 
should  be  safe  under  the  action  of  firing  stresses  and  should  not 
detonate  merely  as  a  result  of  impact  against  obstacles. 

(c)  Not  difficult  to  detonate  with  properly  designed  detonators. 


GUNNERY  AND  EXPLOSIVES.  91 

(d)  Quick  enough  to  give  good  results  when  confined;  shell  fillers 
should  cause  the  projectile  to  break  into  fragments  just  sufficiently 
large  to  put  a  man  or  horse  out  of  action. 

(e)  Convenient  in  form  and  consistency  for  packing  and  loading 
and  for  making  into  charges  of  different  weights. 

16.  Shell  fillers. — In  our  service  picric  acid,  explosive  "D," 
and  tri-nitro- toluol  are  used  as  shell  fillers.     High  explosive  shell 
contain  explosive  "D,"  with  a  small  charge  of  picric  acid  surround- 
ing the  detonator.     High  explosive  shrapnel  has  a  matrix  of  tri- 

.  nitron-toluol,  which  is  detonated  upon  impact  by  the  preliminary 
detonation  of  mercury  fulminate  and  picric  acid;  tri-nitro- toluol  may 
also  be  detonated  with  a  fulminate  detonator  augmented  by  a  small 
amount  of  tri-nitro-toluol  in  loose  crystals. 

17.  Picric  acid. — Picric  acid,  or  tri-nitro-phenol,  is  formed  by 
acting  upon  phenol  with  nitric  acid.     As  a  shell  filler  it  may  be 
pressed  into  the  explosive  cavity  or  melted  and  poured  in;  as  it 
forms  unstable  metallic  salts,  it  must  not  be  assembled  in  pro- 
jectiles until  the  cavity  is  thoroughly  coated  with  a  nonmetallic 
paint.     Picric  acid  is  the  basis  of  many  of  the  foreign  shell  fillers, 
as   for   instance,    melinite,    lyddite,    shimose,    ecrasite,    etc.     The 
difference  in  composition  consists  usually  in  the  addition  of  an 
ingredient   (camphor,    nitro-naphthalene,    djnitro toluene,    etc.)    to 
reduce  the  melting  point. 

17.  Trinitrotoluol. — Trinitrotoluol   is   formed  by  acting  upon 
toluene  with  nitric  acid.     In  its  pure  form  it  may  be  used  as  a  shell 
filler  without  fear  of  the  formation  of  unstable  compounds;  hence  it 
has  been  selected  as  a  matrix  surrounding  the  shrapnel  balls.     Its 
use  is  general  in  high  explosive  shrapnel. 

18.  Other  military  explosives. — There  are  a  number  of  satis- 
factory high  explosives  for  military  use  otker  than  as  shell  fillers. 
These  explosives  conform  to  the  requirements  as  to  stability,  etc. 
The  one  most  easily  obtained  when  needed  would  probably  be 
used. 

Such  explosives  are: 

Gun  cotton; 

Nitroglycerin; 

The  dynamites;' 

Rack  a  rock,  etc. 

Gun  cotton    or   nitrocellulose  is  formed  by  acting  upon  cotton 
with  nitric  acid;   nitroglycerin  is  formed  by  acting  upon  glycerin 


92  GUNNERY  AND  EXPLOSIVES. 

with  nitric  acid.  Due  to  the  danger  involved  in  the  transportation 
of  nitroglycerin,  an  absorbent  was  found  for  it  so  that  it  could  be 
transported  in  solid  form.  When  such  absorbent  is  inert,  it  adds 
nothing  to  the  force  of  the  nitroglycerin ;  when  an  active  absorbent, 
as  for  instance  potassium  nitrate,  is  used,  the  explosion  is  more 
violent. 

Rack  a  rock  is  one  of  the  so-called  safety  mixtures;  in  reality,  the 
components  for  the  manufacture  of  this  high  explosive  are  trans- 
ported separately  to  the  place  where  needed ;  at  this  place  the  mix- 
ture is  made.  The  components  are  powdered  chlorate  of  potassium 
and 'nitrobenzene;  the  chlorate  being  carried  in  small  cloth  car- 
tridges, to  be  dipped  into  the  liquid  nitrobenezene  before  using. 

19.  Fulminate  of  mercury. — This  high  explosive  is  used  in 
detonators  and  is  formed  by  the  action  of  nitric  acid  upon  the  metal 
mercury.  It  is  a  very  powerful  explosive  and  is  the  basis  of  the 
manufacture  of  numerous  types  of  blasting  caps  and  detonators. 
Used  in  service  detonators,  it  is  combined  with  an  alcoholic  solution 
of  shellac  and  assembled  under  a  pressure  somewhat  exceeding  the 
probable  pressure  resulting  from  the  shock  of  discharge.  When  the 
shell  filler  is  properly  confined  and  the  detonator  correctly  propor- 
tioned the  detonation  should  be  perfect;  dense  black  smoke  is  a 
characteristic  of  such  detonation. 

Lead  nitride  has  been  proposed  as  a  substitute  for  mercury  fulmi- 
nate ;  both  trinitrotoluene  and  trinitromethylaniline  have  been  used 
in  the  manufacture  of  detonators. 


APPENDIX  A. 

THE    GREEK   ALPHABET. 


The  Greek  alphabet  is  here  inserted  to  aid  those  who  are  not 
already  familiar  with  it,  in  reading  the  parts  of  the  text  in  which  its 
letters  occur. 


Letters. 

Names. 

Letters. 

Names. 

A  a 

Alpha. 

N   V 

Nu. 

B& 

Beta. 

S  £ 

Xi. 

r  r 

Gamma. 

0  « 

Omicron. 

A  <J 

Delta. 

n  K 

Pi. 

E  e 

Epsilon. 

P  P 

Rho. 

z  C 

Zeta. 

i  ff  ^ 

Sigma. 

H    7) 

Eta. 

T   T 

Tau. 

e  &  e 

Theta. 

r  u 

Upsilon. 

i  > 

Iota. 

9  <}> 

Phi. 

K    K 

Kappa. 

X  X 

Chi. 

A  A 

Lambda. 

¥  $ 

Psi. 

M    fL 

Mu. 

Q  to 

Omega. 

APPENDIX  B. 
Range  table  for  3-inch  field  gun. 


Range. 

Angle  of 
depart- 
ure. 

Angle  of 
depart- 
ure. 

Angle  of 
eleva- 
tion. 

One 
minute, 
in  yards 
of  range. 

One  mil, 
in  yards 
of  range. 

A^  for± 
10  f.  s.  ' 
M.  V. 

A^  forA 
<?=±iV 

Yds. 

o       / 

Mils. 

0          t 

Yds. 

Yds. 

100 

0  05.9 

1.7 

0  00.2 

16.7 

56 

1.08 

0.2 

200 

0  11.9 

3.5 

0  06.2 

15.6 

52 

1.9 

0.8 

300 

0  18.3 

5.4 

0  13.6 

15.2 

50 

2.8 

1.7 

400 

0  24.9 

7.4 

0  19.3 

14.5 

48 

3.7 

3.0 

500 

031.9 

9.5 

0  26.3 

13.9 

46 

4.6 

4.6 

600 

0  39.  0 

11.6 

0  33.4 

13.3 

44 

5.5 

6.9 

700 

0  46.5 

13.8 

0  41.0 

12.7 

.   42 

6.4 

9.4 

800 

0  54.4 

16.1 

0  48.8 

12.2 

41 

7.3 

12.1 

900 

1  02.6 

18.5 

0  57.0 

11.6 

40 

8.1 

15.0 

1,000 

1  11.2 

21.0 

1  05.6 

11.2 

38 

8.8 

18.1 

1,100 

1  20.2 

23.6 

1  14.5 

10.8 

36 

9.5 

21.7 

1,200 

1  29.4 

26.4 

1  23.8 

10.4 

35 

10.2 

25.3 

1,300 

1  39.0 

29.3 

1  33.4 

10.0 

33 

10.8 

29.1 

1,400 

1  49.0 

32.3 

1  43.8 

9.6 

32 

11.4 

32.9 

1,500 

1  59.4 

35.4 

1  53.8 

9.4 

31 

12.1 

36.9 

1,600 

2  10.3 

38.6 

2  04.7 

9.2 

31 

12.7 

41.2 

1,700 

2  21.5 

41.9 

2  15.9 

9.0 

30 

13.3 

45.5 

1,800 

2  32.9 

45.3 

2  27.3 

8.8 

29 

13.9 

49.8 

1,900 

2  44.7 

48.8 

2  39.1 

8.5 

28 

14.5 

54.1 

2,000 

2  56.7 

52.4 

2  51.1 

8.3 

27 

15.0 

58.4 

2,100 

3  09.3 

56.1 

3  03.7 

8.0 

27 

15.5 

62.9 

2,200 

.3  22.1 

59.9 

3  16.5 

7.8 

26 

16.0 

67.4 

2,300 

3  35.1 

63.8 

3  29.5 

7.7 

26 

16.4 

71.9 

2,400 

3  48.3 

67.7 

3  42.7 

7.6 

25 

16.9 

76.5 

2,500 

401.8 

71.7 

3  56.2 

7.4 

25 

17.3 

81.0 

2,600 

4  15.4 

75.7 

4  08.7 

7.3 

24 

17.7 

85.3 

2,700 

4  29.  1 

79.8 

4  22.7 

7.1 

24 

18.1 

89.7 

2,800 

4  43.  1 

83.9 

4  36.7 

7.0 

23 

18.5 

94.1 

2,900 

4  57.5 

88.1 

4  50.9 

6.9 

23 

18.9 

98.5 

3,000        5  12.0 

92.4 

505.4 

6.8 

23 

19.2 

102.9 

94 


APPENDIX  B. 

Range  table  for  3-inch  field  gun. 


AX  for 
wind  10 
miles  per 
hour. 

Drift. 

Deviation 
for  10 
miles 
cross 
wind. 

Angle  of 
fall. 

Slope  of 
fall. 

Time  of 
flight. 

Terminal 
velocity. 

Maxi- 
mum 
ordinate. 

Yds. 

Yds. 

Yds. 

0             / 

1  on— 

Sees. 

F.S. 

Feet. 

0.01 

0.4 

0.04 

0  05.8 

592.7 

0.18 

1,  647.  0 

0.2 

0.06 

0.7 

0.08 

0  12.2 

281.1 

0.36 

1,  595.  4 

0.8 

0.12 

1.0 

0.12 

0  19.3 

178.0 

0.55 

1,  547.  0 

1.7 

0.26 

1.2 

0.16 

0  27.0 

127.3 

0.75 

1,500.0 

2.9 

0.43 

1.5 

0.21 

0  35.3 

99.9 

0.96 

1,456.0 

4.3 

0.65 

1.7 

0.27 

0  44.2 

87.5 

1.17 

1,414.0 

6.0 

0.89 

1.9 

0.32 

0  53.9 

75.2 

1.38 

1,374.2 

8.1 

1.20 

2.1 

0.38 

1  04.3 

63.1 

1.60 

1,337.3 

10.7 

1.50 

2.4 

0.44 

1  15.  5 

51.3 

1.83 

1,303.0 

13.8 

1.80 

2.6 

0.50 

1  27.3 

39.4 

2.07 

1,270.2 

17.3 

2.20 

2.8 

0.67 

1  40:8 

35.8 

2.31 

1,242.0 

21.7 

2.60 

3.1 

0.85 

1  54.6 

32.0 

2.56 

1,217.0 

26.6 

3.10 

3.3 

1.10 

2  08.9 

27.2 

2.81 

1,  193.  0 

32.1 

3.50 

3.6 

1.30 

2  23.6 

24.5 

3.07 

1,168.0 

38.3 

4.00 

3.9 

1.50 

2  38.6 

21.6 

3.34 

1,145.0 

45.3 

4.50 

4.2 

1.70 

2  55.6 

19.8 

3.61 

1,121.0 

53.1 

5.10 

4.4 

2.00 

3  13.0 

18.1 

3.89 

1,099.0 

61.8 

5.60 

4.7 

2.30 

3  30.8 

16.5 

4.17 

1,078.0 

71.4 

6.20 

4.9 

2.60 

3  49.0 

15.1 

4.46 

1,057.0 

81.8 

6.80 

5.1 

2.90 

4  07.6 

13.9 

4.75 

1,038.0 

93.1 

7.40 

5.3 

3.20 

4  26.9 

12.9 

5.05 

1,020.0 

105.3 

8.00 

5.6 

3.50 

4  46.7 

12.1 

5.35 

1,002.0 

118.4 

8.60 

5.8 

3.90 

5  06.9 

11.3 

5.65 

986.0 

132.5 

9.30 

6.2 

4.30 

5  27.6 

10.5 

5.95 

971.0 

147.5 

9.90 

6.6 

4.60 

5  48.8 

9.8 

6.26 

958.0 

163.5 

10.60 

7.0 

5.00 

6  10.4 

9.3 

6.57 

946.0 

180.0 

11.20 

7.5 

5.40 

6  32.5 

8.8 

6.88 

935.0 

198.0 

11.80 

8.0 

5.90 

6  55.0 

8.3 

7.19 

924.0 

216.0 

12.50 

8.5 

6.40 

7  17.9 

7.8 

7.51 

915.0 

236.0 

13.10 

9.1 

6.90 

7  41.2 

7.4 

7.83          906.0 

257.0 

95 


96  GUNNERY  AND  EXPLOSIVES. 

Range  table  for  3-inch  field  gun — Continued. 


Range. 

Angle  of 
depart- 
ure. 

Angle  of 
depart- 
ure. 

Angle  of 
eleva- 
tion. 

One 

minute, 
in  yards 
of  range. 

One  mil, 
in  yards 
of  range. 

&X  for± 
10  f.  s. 
M.  V. 

A^TforA 
'tf-iA. 

Yds. 

0            f 

Mils. 

o          / 

Yds. 

Yds. 

3,100 

5  26.6 

96.8 

5  20.0 

6.7 

22 

19.5 

107.1 

3,200 

5  41.6 

101.3 

5  35.0 

6.6 

22 

19.8 

111.3 

3,300 

5  56.9 

105.9 

5  50.3 

6.5 

22 

20.1 

115.5 

3,400 

6  12.6 

110.5 

6  06.0 

6.3 

21 

20.4 

119.7 

3,500 

628.7 

115.2 

622.1 

6.1 

21 

20.6 

123.9 

3,600 

6  45.1 

120.0 

6  38.5 

6.0 

20 

20.8 

127.8 

3,700 

7  01.9 

124.9 

6  55.2 

5.9 

20 

21.0 

131.8 

3,800 

7  19.0 

130.0 

7  12.4 

5.7 

19 

21.2 

136.0 

3.900 

7  36.5 

135.2 

7  29.8 

5.6 

19 

21.4 

140.3 

4,000 

7  54.2 

140.5 

7  47.5 

5.5 

18 

21.6 

144.8 

4,100 

8  12.3 

145.9 

8  05.9 

5.4 

18 

21.8 

149.6 

4,200 

8  30.7 

151.4 

8  24.0 

5.3 

18 

22.0 

154.5 

4,300 

8  49.5 

157.0 

8  42.9 

5.2 

17 

22.2 

159.4 

4,400 

9  08.6 

162.6 

9  01.9 

5.2 

17 

22.4 

164.4 

4,500 

928.5 

168.3 

9  21.8 

5.1 

17 

22.6 

169.5 

4,600 

9  47.7 

174.1 

9  41.9 

5.0 

17 

22.8 

174.8 

4,700 

10  07.  8 

180.0 

10  02.  0 

4.9 

16 

23.0 

180.1 

4,800 

10  28.  2 

186.0 

10  22.  4 

4.8 

16 

23.2 

185.4 

4,900 

10  49.  0 

192.2 

10  43.  2 

4.7 

16 

23.4 

190.8 

5,000 

11  10.1 

198.5 

11  04.3 

4.7 

16 

23.6 

196.3 

5,100 

11  31.5 

204.9 

11  25.  7 

4.6 

15 

23.8 

201.4 

5,200 

11  53.3 

211.4 

11  47.  5 

4.5 

15 

24.0 

206.5 

5,300 

12  15.5 

218.0 

12  09.7 

4.4 

15 

24.2 

211.6 

5,400 

12  38.  1 

224.7 

12  32.  3 

4.3 

14 

24.4 

216.6 

5,500 

13  01.1 

231.5 

12  55.3 

43 

14 

24.6 

221.7 

5,600 

13  24.  4 

238.4 

13  17.7 

4.2 

14 

24.8 

226.6 

5,700 

13  48.  2 

245.4 

13  40.  5 

4.1 

14 

25.0 

231.6 

5,800 

14  12.3 

252.5 

14  04.  6 

4.1 

14 

25.2 

236.5 

5,900 

14  36.  9 

259.8 

14  29.  2 

4.0 

13 

25.3 

241.5 

6,000 

15  01.8 

267.2 

14  54.1 

4.0 

13 

25.5 

246.6 

6,100 

15  27.  1 

274.7 

15  19.4 

3.9 

13 

25.7 

251.6 

6,200 

15  52.  9 

282.3 

15  45.  2 

3.8 

13 

25.8 

256.6 

6,300 

16  19.0 

290.0 

16  11.3 

3.8 

13 

26.0 

261.6 

6,400 

16  45.  6 

297.8 

16  37.  9 

3.7 

12 

26.1 

266.6 

6,500 

17  12.6 

305.8 

17  04.9 

3.7 

12 

26.2 

271.6 

GUNNERY  AND  EXPLOSIVES. 

Range  table  for  3-inch  field  gun — Continued. 


97 


&X  for 
wind  10 
miles  per 
hour. 

Drift. 

Deviation 
for  10 
miles 
cross 
wind. 

Angle  of 
Ml. 

Slope  of 
fall. 

Time  of 
flight. 

Terminal 
velocity. 

Maxi- 
mum 
ordinate. 

Yds. 

Yds. 

Yds. 

o       , 

Ion  — 

Sees. 

F.  S. 

Feet. 

13.80 

9.8 

7.40 

8  04.2 

7.1 

8.15 

899.0 

279.0 

14.40 

10.6 

8.00 

8  28.0 

6.7 

8.47 

892.0 

302.0 

15.00 

11.6 

8.60 

8  52.5 

6.4 

8.80 

886.0 

326.0 

15.70 

12.6 

9.20 

9  17.7 

6.1 

9.13 

879.0 

351.0 

16.40 

13.6 

9.80 

9  43.7 

5.8 

9.47 

873.0 

378.0 

17.00 

14.7 

10.50 

10  10.  4 

5.6 

9.82 

865.0 

406.0 

17.70 

15.7 

11.10 

10  37.  6 

5.2 

10.17 

858.0 

436.  0 

18.40 

16.6 

11.80 

11  05.  4 

5.0 

10.53 

851.0 

468.0 

19.20 

17.5 

12.50 

11  33.9 

.8 

10.89 

844.0 

501.0 

19.90 

18.4 

13.30 

12  02.9 

'.  :.7 

11.25 

837.0 

536.0 

20.70 

19.3. 

14.00 

12  32.  6 

.5 

11.62 

830.0 

572.0 

21.60 

20.1 

14.80 

13  02.9 

.3 

11.99 

824.0 

610.0 

22.40 

20.9 

15.60 

13  33.  8 

4,1 

12.37 

818.0 

649.0 

23.20 

21/7 

16.40 

14  05.  2 

4.0 

12.75 

812.0 

689.0 

24.00 

22.5 

17.80 

14  37.3 

3.8 

13.13 

806.0 

731.0 

25.00 

23.4 

18.20 

15  09.  9 

3.7 

13.52 

800.0 

775.0 

26.00 

24.4 

19.10 

15  43.  1 

3.6 

13.92 

795.0 

822.0 

27.00 

25.3 

20.00 

16  16.8 

3.4 

14.32 

789.0 

871.0 

28.00 

26.3 

20.90 

16  51.1 

3.3 

14.72 

784.0 

922.0 

29.00 

27.7 

21.90 

17  26.0 

3.2 

15.12 

779.0 

975.0 

29.80 

29.2 

22.80 

18  01.  9 

3.1 

15.52 

774.0 

1,029.0 

30.70 

81.1 

23.80 

18  38.  2 

3.0 

15.92 

770.0 

1,085.0 

31.50 

33.4 

24.80 

19  14.8 

2.9 

16.32 

765.0 

'1,143.0 

32.40 

36.0 

25.80 

19  51.7 

2.8 

16.73 

761.0 

1,202.0 

33.40 

38.8 

26.90 

20  29.0 

2.7 

17.14 

757.0 

1,263.0 

34.40 

41.8 

28.00 

21  06.  3 

2.6 

17.  56 

753.0 

1,326.0 

35.50 

45.0 

29.10 

21  44.1 

2.5 

18.00 

750.0 

1,391.0 

36.60 

48.8 

30.30 

22  22.  5 

2.4 

18.44 

747.0 

1,  458.  0 

37.70 

51.8 

31.60 

23  01.  6 

2.3 

18.89 

743.0 

1,527.0 

38.80 

55.3 

32.80 

23  40.9 

2.3 

19.36 

740.0 

1,598.0 

39.90 

59.0 

34.20 

24  20.  9 

2.2 

19.85 

737.0 

1,672.0 

41.10 

62.5 

35.60 

25  01.  5 

2.2 

20.35 

733.0 

1,  748.  0 

42.30 

66.1 

37.00 

25  42.  7 

2.1 

20.86 

730.0 

1,827.0 

43.60 

69.5 

38.80 

26  24.  5 

2.1 

21.38 

727.0 

1,908.0 

44.80 

73.0 

39.90 

27  06.8 

1.9 

21.  S2 

724.0 

1,992.0 

APPENDIX  C. 

EXAMINATION    QUESTIONS. 

How  is  the  force  of  recoil  checked  in  the  3-inch  field  gun?  What 
is  the  purpose  of  the  counter-recoil  buffer?  Describe  the  mode  of 
action  of  the  counter-recoil  buffer.  What  precautions  should  be 
taken  in  filling  the  cylinder? 

What  projectiles  are  used  in  the  3-inch  field  gun?  Describe  each 
kind. 

The  drill  regulations  prescribe  that  the  gunner  shall  set  off  the 
range,  even  though  he  is  only  laying  for  direction.  Why  is  this 
necessary? 

What  conditions  must  be  fulfilled  before  the  battery  commander's 
telescope  is  in  adjustment?  Describe  the  methods  of  making  the 
adjustment  and  show  that  the  methods  described  accomplish  the 
purpose. 

What  is  the  .composition  of  black  gunpowder?  What  is  the  pur- 
pose of  each  constituent? 

Describe,  in  general  terms,  the  process  of  manufacture  of  smoke- 
less powder. 

What  is  the  purpose  of  the  priming  charge  of  black  powder  which 
is  added  to  the  smokeless  powder  charge? 

What  is  the  object  of  perforating  the  grains  of  smokeless  powder? 

What  is  the  advantage  of  a  "slow-burning"  powder  over  a  " quick- 
burning  "  powder?  What  is  the  difference  between  the  action  of  a 
"high  explosive"  and  that  of  a  "propelling"  charge? 

When  is  a  "correction  for  obliquity"  necessary? 

What  is  the  principle  of  "the  rigidity  of  the  trajectory"?  What 
is  the  practical  effect  of  this  principle  in  gunnery? 

A  battery  is  in  position.  A  suitable  observing  station  has  been 
chosen  in  rear  of  the  battery  and  on  the  prolongation  of  the  line 
joining  the  right  gun  and  the  target.  The  range  to  the  target  from 
the  observing  station  has  been  found  to  be  3,000  y^.rds,  the  distance 
from  the  observing  station  to  the  gun  is  100  yards.  A  suitable 


GUNNERY  AND  EXPLOSIVES.  99 

aiming  point  has  been  selected  and  its  distance  from  the  observing 
station  determined  as  2,000  yards.  Measurement  of  the  angle  at 
the  observing  station  between  the  aiming  point  and  the  target  gives 
1,800  mils.  What  is  the  deflection  of  the  right  gun? 

What  are  the  mathematical  operations  performed  by  the  "  sliding 
scale"  on  the  battery,  commander's  ruler  when  it  is  used  to  deter- 
mine the  height  of  the  trajectory  at  the  mask? 

A  battery  fires  its  first  salvo  and  it  is  seen  that  all  bursts  are  on 
graze.  The  battery  commander  wishes  to  adjust  the  height  of 
bursts  without  changing  the  angle  of  site.  By  how  much  should 
he  change  the  corrector?  Why? 

A  battery  is  firing  at  a  target  the  range  of  which  is  5,000  yards. 
What  change  in  range  will  be  caused  by  a  change  in  the  angle  of 
site  of  15  mils? 

What  is  the  maximum  slope  of  fall  of  the  lower  elements  of  the 
shrapnel  sheaf  at  3,000  yards  range? 

Define  range,  angle  of  departure,  angle  of  site,  remaining  velocity. 

What  is  the  deflection  of  the  right  piece  of  a  battery,  using  indirect 
laying,  with  an  aiming  point  in  front  and  5,000  yards  distant,  the 
range  being  4,000  yards,  the  observing  station  being  on  the  left  of 
the  guns  and  200  yards  from  the  right  gun,  the  angle  measured  at 
the  observing  station  from  the  aiming  point  to  target  being  6,230? 
How  did  you  get  it? 

What  are  the  principal  sources  of  error  in  field  artillery  service 
practice? 

How  would  you  determine  in  the  general  case  whether  you  could 
fire  over  a  mask?  Would  the  projectiles  clear  the  crest,  if  a  battery 
was  firing  from  a  position  200  yards  in  rear  of  it,  upon  a  target  2,000 
yards  from  the  gun,  and  having  an  angle  of  site  of  315,  the  interven- 
ing crest  being  24  feet  above  the  guns? 

If  your  B.C.  telescope  and  B.C.  ruler  were  both  lost  or  unservice- 
able, how  would  you  determine  firing  data  for  indirect  laying? 

What  is  the  corrector  used  for?  Does  an  increase  of  the  corrector 
have  any  effect  on  the  trajectory  of  a  shrapnel?  Within  effective 
artillery  ranges  does  a  change  of  range  have  any  effect  on  the  cor- 
rector for  the  day? 

Using  the  B.C.  ruler,  construct  to  scale  on  cross  section  paper  the 
trajectory  for  range  3,500  yards. 

What  is  the  principal  characteristic  of  a  perfect  detonation? 


100  GUNNERY  AND  EXPLOSIVES. 

In  the  adjustment  of  fire,  what  times  enter  into  the  total  time 
from  opening  fire  to  the  delivery  of  the  first  effective  shrapnel? 

Why  has  the  one  mil  height  of  burst  during  adjustment  been 
adopted  in  our  service?  Is  this  height  of  burst  correct  for  all  ranges? 
Gives  reasons  for  your  answer. 

What  is  the  usual  procedure  in  ranging?  Why  should  changes  of 
range  less  than  25  yards  never  be  made? 

Describe  briefly  what  occurs  when  a  gun  is  fired. 

What  are  the  principal  errors  affecting  the  accuracy  of  fire? 

What  is  the  50  per  cent  zone? 

What  is  the  line  of  sight  in  indirect  laying? 

Construct  on  cross  section  paper  the  ground  section  of  the  cone  of 
dispersion  of  a  service  shrapnel  bursting  at  3,500  yards  range. 


Appendix  D 
Geometrical  illustration  of  parallax  me  food 


Case  - 


>       '  /-  arm  /  >/7  OOpOJ/fC.  Side* 

r/>  ^  Ife  *ftf96 

,\  "B  T,  parallel  to  6  T 

Z/-'J    ',  SP.  paraf/e/ to  GP 
' '  f          A  -  B-nP-n  T 


v/y  ft> 


2d  Case  - 
Pand  Ton  opposh 
BG,  B  t-o  left  of  G 


,'r    3d  Case- 
•"  P and  Ton  same  s/dc  of  BGi 
,,''       BtonyhtofG 


1.  A-Btn(-T>-T) 

2.  *B-n(-P-T) 


.0 


101 


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'"~"  •*'*•"  --S  -.~.:  ^i 

V  A  • 
•  A 


U.C.  BERKELEY  LIBRARIES 


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